https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Seeger&feedformat=atomUW-Math Wiki - User contributions [en]2020-07-11T21:03:51ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=19273Analysis Seminar2020-03-17T16:12:52Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wick<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Ziming Shi<br />
| UW Madison<br />
|[[#linktoabstract |On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|Canceled<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|Canceled<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|Canceled<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|Canceled<br />
|Ruixiang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|Canceled<br />
| Brian<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|Canceled<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|Canceled<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
===Tamás Titkos===<br />
<br />
<b>Isometries of Wasserstein spaces</b><br />
<br />
Due to its nice theoretical properties and an astonishing number of applications via optimal transport problems, probably the most intensively studied metric nowadays is the $p$-Wasserstein metric. Given a complete and separable metric space $X$ and a real number $p\geq1$, one defines the $p$-Wasserstein space $\mathcal{W}_p(X)$ as the collection of Borel probability measures with finite $p$-th moment, endowed with a distance which is calculated by means of transport plans.<br />
<br />
The main aim of our research project is to reveal the structure of the isometry group $\mathrm{Isom}(\mathcal{W}_p(X))$. Although $\mathrm{Isom}(X)$ embeds naturally into $\mathrm{Isom}(\mathcal{W}_p(X))$ by push-forward, and this embedding turned out to be surjective in many cases, these two groups are not isomorphic in general. Recently, Kloeckner described the isometry group of the quadratic Wasserstein space over the real line. It turned out that this group is extremely rich: it contains a flow of wild behaving isometries that distort the shape of measures. Following this line of investigation, we described $\mathrm{Isom}(\mathcal{W}_p(\mathbb{R}))$ and $\mathrm{Isom}(\mathcal{W}_p([0,1])$ for all $p\geq 1$. In this talk I will survey first some of the earlier results in the subject, and then I will present the key results of our recent manuscript \emph{"Isometric study of Wasserstein spaces -- The real line"} (to appear in Trans. Amer. Math. Soc., arXiv:2002.00859).<br />
<br />
Joint work with György Pál Gehér (University of Reading) and Dániel Virosztek (IST Austria).<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=19272Analysis Seminar2020-03-17T16:11:17Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wick<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Ziming Shi<br />
| UW Madison<br />
|[[#linktoabstract |On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|Canceled<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|Canceled<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|Canceled<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|Canceled<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|Canceled<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|Canceled<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|Canceled<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
===Tamás Titkos===<br />
<br />
<b>Isometries of Wasserstein spaces</b><br />
<br />
Due to its nice theoretical properties and an astonishing number of applications via optimal transport problems, probably the most intensively studied metric nowadays is the $p$-Wasserstein metric. Given a complete and separable metric space $X$ and a real number $p\geq1$, one defines the $p$-Wasserstein space $\mathcal{W}_p(X)$ as the collection of Borel probability measures with finite $p$-th moment, endowed with a distance which is calculated by means of transport plans.<br />
<br />
The main aim of our research project is to reveal the structure of the isometry group $\mathrm{Isom}(\mathcal{W}_p(X))$. Although $\mathrm{Isom}(X)$ embeds naturally into $\mathrm{Isom}(\mathcal{W}_p(X))$ by push-forward, and this embedding turned out to be surjective in many cases, these two groups are not isomorphic in general. Recently, Kloeckner described the isometry group of the quadratic Wasserstein space over the real line. It turned out that this group is extremely rich: it contains a flow of wild behaving isometries that distort the shape of measures. Following this line of investigation, we described $\mathrm{Isom}(\mathcal{W}_p(\mathbb{R}))$ and $\mathrm{Isom}(\mathcal{W}_p([0,1])$ for all $p\geq 1$. In this talk I will survey first some of the earlier results in the subject, and then I will present the key results of our recent manuscript \emph{"Isometric study of Wasserstein spaces -- The real line"} (to appear in Trans. Amer. Math. Soc., arXiv:2002.00859).<br />
<br />
Joint work with György Pál Gehér (University of Reading) and Dániel Virosztek (IST Austria).<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=19265Analysis Seminar2020-03-13T00:56:52Z<p>Seeger: /* Yifei Pan */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wick<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Ziming Shi<br />
| UW Madison<br />
|[[#linktoabstract |On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|Canceled<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|Canceled<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|Canceled<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|Canceled<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|Canceled<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|Canceled<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
===Tamás Titkos===<br />
<br />
<b>Isometries of Wasserstein spaces</b><br />
<br />
Due to its nice theoretical properties and an astonishing number of applications via optimal transport problems, probably the most intensively studied metric nowadays is the $p$-Wasserstein metric. Given a complete and separable metric space $X$ and a real number $p\geq1$, one defines the $p$-Wasserstein space $\mathcal{W}_p(X)$ as the collection of Borel probability measures with finite $p$-th moment, endowed with a distance which is calculated by means of transport plans.<br />
<br />
The main aim of our research project is to reveal the structure of the isometry group $\mathrm{Isom}(\mathcal{W}_p(X))$. Although $\mathrm{Isom}(X)$ embeds naturally into $\mathrm{Isom}(\mathcal{W}_p(X))$ by push-forward, and this embedding turned out to be surjective in many cases, these two groups are not isomorphic in general. Recently, Kloeckner described the isometry group of the quadratic Wasserstein space over the real line. It turned out that this group is extremely rich: it contains a flow of wild behaving isometries that distort the shape of measures. Following this line of investigation, we described $\mathrm{Isom}(\mathcal{W}_p(\mathbb{R}))$ and $\mathrm{Isom}(\mathcal{W}_p([0,1])$ for all $p\geq 1$. In this talk I will survey first some of the earlier results in the subject, and then I will present the key results of our recent manuscript \emph{"Isometric study of Wasserstein spaces -- The real line"} (to appear in Trans. Amer. Math. Soc., arXiv:2002.00859).<br />
<br />
Joint work with György Pál Gehér (University of Reading) and Dániel Virosztek (IST Austria).<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=19264Analysis Seminar2020-03-13T00:56:32Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wick<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Ziming Shi<br />
| UW Madison<br />
|[[#linktoabstract |On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|Canceled<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|Canceled<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|Canceled<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|Canceled<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|Canceled<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|Canceled<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
<br />
===Tamás Titkos===<br />
<br />
<b>Isometries of Wasserstein spaces</b><br />
<br />
Due to its nice theoretical properties and an astonishing number of applications via optimal transport problems, probably the most intensively studied metric nowadays is the $p$-Wasserstein metric. Given a complete and separable metric space $X$ and a real number $p\geq1$, one defines the $p$-Wasserstein space $\mathcal{W}_p(X)$ as the collection of Borel probability measures with finite $p$-th moment, endowed with a distance which is calculated by means of transport plans.<br />
<br />
The main aim of our research project is to reveal the structure of the isometry group $\mathrm{Isom}(\mathcal{W}_p(X))$. Although $\mathrm{Isom}(X)$ embeds naturally into $\mathrm{Isom}(\mathcal{W}_p(X))$ by push-forward, and this embedding turned out to be surjective in many cases, these two groups are not isomorphic in general. Recently, Kloeckner described the isometry group of the quadratic Wasserstein space over the real line. It turned out that this group is extremely rich: it contains a flow of wild behaving isometries that distort the shape of measures. Following this line of investigation, we described $\mathrm{Isom}(\mathcal{W}_p(\mathbb{R}))$ and $\mathrm{Isom}(\mathcal{W}_p([0,1])$ for all $p\geq 1$. In this talk I will survey first some of the earlier results in the subject, and then I will present the key results of our recent manuscript \emph{"Isometric study of Wasserstein spaces -- The real line"} (to appear in Trans. Amer. Math. Soc., arXiv:2002.00859).<br />
<br />
Joint work with György Pál Gehér (University of Reading) and Dániel Virosztek (IST Austria).<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=19263Analysis Seminar2020-03-13T00:55:39Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wick<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Purdue University Fort Wayne<br />
|[[#linktoabstract |On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|Canceled<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|Canceled<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|Canceled<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|Canceled<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|Canceled<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|Canceled<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
<br />
===Tamás Titkos===<br />
<br />
<b>Isometries of Wasserstein spaces</b><br />
<br />
Due to its nice theoretical properties and an astonishing number of applications via optimal transport problems, probably the most intensively studied metric nowadays is the $p$-Wasserstein metric. Given a complete and separable metric space $X$ and a real number $p\geq1$, one defines the $p$-Wasserstein space $\mathcal{W}_p(X)$ as the collection of Borel probability measures with finite $p$-th moment, endowed with a distance which is calculated by means of transport plans.<br />
<br />
The main aim of our research project is to reveal the structure of the isometry group $\mathrm{Isom}(\mathcal{W}_p(X))$. Although $\mathrm{Isom}(X)$ embeds naturally into $\mathrm{Isom}(\mathcal{W}_p(X))$ by push-forward, and this embedding turned out to be surjective in many cases, these two groups are not isomorphic in general. Recently, Kloeckner described the isometry group of the quadratic Wasserstein space over the real line. It turned out that this group is extremely rich: it contains a flow of wild behaving isometries that distort the shape of measures. Following this line of investigation, we described $\mathrm{Isom}(\mathcal{W}_p(\mathbb{R}))$ and $\mathrm{Isom}(\mathcal{W}_p([0,1])$ for all $p\geq 1$. In this talk I will survey first some of the earlier results in the subject, and then I will present the key results of our recent manuscript \emph{"Isometric study of Wasserstein spaces -- The real line"} (to appear in Trans. Amer. Math. Soc., arXiv:2002.00859).<br />
<br />
Joint work with György Pál Gehér (University of Reading) and Dániel Virosztek (IST Austria).<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=19166Analysis Seminar2020-02-28T16:02:51Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wick<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Purdue University Fort Wayne<br />
|[[#linktoabstract | On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=19165Analysis Seminar2020-02-28T16:02:30Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wic<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Purdue University Fort Wayne<br />
|[[#linktoabstract | On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18790Analysis Seminar2020-01-24T22:25:06Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18789Analysis Seminar2020-01-24T21:44:04Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18788Colloquia2020-01-24T21:43:25Z<p>Seeger: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31 <br />
|[https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke)<br />
|[[#Lillian Pierce (Duke) |On Bourgain’s counterexample for the Schrödinger maximal function]]<br />
|Marshall/Seeger<br />
|-<br />
|Feb 7<br />
|Joe Kileel (Princeton)<br />
|[[TBA]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|Cynthia Vinzant (NCSU)<br />
|[[TBA]]<br />
|Roch/Erman<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
=== Lillian Pierce (Duke) ===<br />
<br />
Title: On Bourgain’s counterexample for the Schrödinger maximal function<br />
<br />
Abstract: In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space $H^s$ must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.” <br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18787Analysis Seminar2020-01-24T21:41:32Z<p>Seeger: /* Lillian Pierce */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18786Analysis Seminar2020-01-24T21:40:37Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18783Colloquia2020-01-24T17:23:40Z<p>Seeger: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|-<br />
|Jan 31<br />
|[reserved]<br />
|-<br />
|Feb 7<br />
|Joe Kileel (Princeton)<br />
|[[TBA]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|Cynthia Vinzant (NCSU)<br />
|[[TBA]]<br />
|Roch/Erman<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18782Colloquia2020-01-24T17:21:54Z<p>Seeger: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|<br />
|Jan 31<br />
|[reserved]<br />
|-<br />
|Feb 7<br />
|Joe Kileel (Princeton)<br />
|[[TBA]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|Cynthia Vinzant (NCSU)<br />
|[[TBA]]<br />
|Roch/Erman<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=18781Colloquia2020-01-24T17:21:22Z<p>Seeger: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer (LSU)<br />
|[[#Andrew Zimmer (LSU)| "Intrinsic and extrinsic geometries in several complex variables"]]<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan (MIT)<br />
|[[#Charlotte Chan (MIT)|"Flag varieties and representations of p-adic groups"]]<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday 2:30-3:30pm Room 911'''<br />
|Alex Waldron (Michigan)<br />
|[[#Alex Waldron (Michigan)|Gauge theory and geometric flows]]<br />
|Paul<br />
|-<br />
|Dec 11 '''Wednesday 4-5pm'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|-<br />
|Dec 13 <br />
|Chenxi Wu (Rutgers)<br />
|[[#Chenxi Wu (Rutgers)|Kazhdan's theorem on metric graphs]]<br />
|Ellenberg<br />
|-<br />
|Dec 18 '''Wednesday 4-5pm'''<br />
|Ruobing Zhang (Stony Brook)<br />
|[[#Ruobing Zhang (Stony Brook)|Geometry and analysis of degenerating Calabi-Yau manifolds]]<br />
|Paul<br />
|-<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 10<br />
|Thomas Lam (Michigan) <br />
|[[#Thomas Lam (Michigan) |Positive geometries and string theory amplitudes]]<br />
|Erman<br />
|-<br />
|Jan 21 '''Tuesday 4-5 pm in B139'''<br />
|[http://www.nd.edu/~cholak/ Peter Cholak] (Notre Dame) <br />
|[[#Peter Cholak (Notre Dame) |What can we compute from solutions to combinatorial problems?]]<br />
|Lempp<br />
|-<br />
|Jan 24<br />
|[https://math.duke.edu/people/saulo-orizaga Saulo Orizaga] (Duke)<br />
|[[#Saulo Orizaga (Duke) | Introduction to phase field models and their efficient numerical implementation ]]<br />
|<br />
|-<br />
|Jan 27 '''Monday 4-5 pm'''<br />
|[https://math.yale.edu/people/caglar-uyanik Caglar Uyanik] (Yale)<br />
|[[#Caglar Uyanik (Yale) | Hausdorff dimension and gap distribution in billiards ]]<br />
|Ellenberg<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|[[#Andy Zucker (Lyon) |Topological dynamics of countable groups and structures]]<br />
|Soskova/Lempp<br />
|<br />
|Jan 31<br />
|reserved]<br />
|-<br />
|Feb 7<br />
|Joe Kileel (Princeton)<br />
|[[TBA]]<br />
|Roch<br />
|-<br />
|Feb 10<br />
|Cynthia Vinzant (NCSU)<br />
|[[TBA]]<br />
|Roch/Erman<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 23<br />
|Martin Hairer (Imperial College London)<br />
|Wolfgang Wasow Lecture<br />
|Hao Shen<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
=== Alex Waldron (Michigan) ===<br />
<br />
Title: Gauge theory and geometric flows<br />
<br />
Abstract: I will give a brief introduction to two major areas of research in differential geometry: gauge theory and geometric flows. I'll then introduce a geometric flow (Yang-Mills flow) arising from a variational problem with origins in physics, which has been studied by geometric analysts since the early 1980s. I'll conclude by discussing my own work on the behavior of Yang-Mills flow in the critical dimension (n = 4).<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
=== Chenxi Wu (Rutgers) ===<br />
<br />
Title: Kazhdan's theorem on metric graphs<br />
<br />
Abstract: I will give an introduction to the concept of canonical (arakelov) metric on a metric graph, which is related to combinatorial questions like the counting of spanning trees, and generalizes the corresponding concept on Riemann surfaces. I will also present a recent result in collaboration with Farbod Shokrieh on the convergence of canonical metric under normal covers.<br />
<br />
=== Ruobing Zhang (Stony Brook) ===<br />
<br />
Title: Geometry and analysis of degenerating Calabi-Yau manifolds<br />
<br />
Abstract: This talk concerns a naturally occurring family of degenerating Calabi-Yau manifolds. A primary tool in analyzing their behavior is to combine the recently developed structure theory for Einstein manifolds and multi-scale singularity analysis for degenerating nonlinear PDEs in the collapsed setting. Based on the algebraic degeneration, we will give precise and more quantitative descriptions of singularity formation from both metric and analytic points of view.<br />
<br />
=== Thomas Lam (Michigan) === <br />
<br />
Title: Positive geometries and string theory amplitudes<br />
<br />
Abstract: Inspired by developments in quantum field theory, we<br />
recently defined the notion of a positive geometry, a class of spaces<br />
that includes convex polytopes, positive parts of projective toric<br />
varieties, and positive parts of flag varieties. I will discuss some<br />
basic features of the theory and an application to genus zero string<br />
theory amplitudes. As a special case, we obtain the Euler beta<br />
function, familiar to mathematicians, as the "stringy canonical form"<br />
of the closed interval.<br />
<br />
This talk is based on joint work with Arkani-Hamed, Bai, and He.<br />
<br />
=== Peter Cholak (Notre Dame) ===<br />
<br />
Title: What can we compute from solutions to combinatorial problems?<br />
<br />
Abstract: This will be an introductory talk to an exciting current <br />
research area in mathematical logic. Mostly we are interested in <br />
solutions to Ramsey's Theorem. Ramsey's Theorem says for colorings <br />
C of pairs of natural numbers, there is an infinite set H such that <br />
all pairs from H have the same constant color. H is called a homogeneous <br />
set for C. What can we compute from H? If you are not sure, come to <br />
the talk and find out!<br />
<br />
=== Saulo Orizaga (Duke) ===<br />
<br />
Title: Introduction to phase field models and their efficient numerical implementation<br />
<br />
Abstract: In this talk we will provide an introduction to phase field models. We will focus in models<br />
related to the Cahn-Hilliard (CH) type of partial differential equation (PDE). We will discuss the<br />
challenges associated in solving such higher order parabolic problems. We will present several<br />
new numerical methods that are fast and efficient for solving CH or CH-extended type of problems.<br />
The new methods and their energy-stability properties will be discussed and tested with several computational examples commonly found in material science problems. If time allows, we will talk about more applications in which phase field models are useful and applicable.<br />
<br />
=== Caglar Uyanik (Yale) ===<br />
<br />
Title: Hausdorff dimension and gap distribution in billiards<br />
<br />
Abstract: A classical “unfolding” procedure allows one to turn questions about billiard trajectories in a Euclidean polygon into questions about the geodesic flow on a surface equipped with a certain geometric structure. Surprisingly, the flow on the surface is in turn related to the geodesic flow on the classical moduli spaces of Riemann surfaces. Building on recent breakthrough results of Eskin-Mirzakhani-Mohammadi, we prove a large deviations result for Birkhoff averages as well as generalize a classical theorem of Masur on geodesics in the moduli spaces of translation surfaces. <br />
<br />
=== Andy Zucker (Lyon) ===<br />
<br />
Title: Topological dynamics of countable groups and structures<br />
<br />
Abstract: We give an introduction to the abstract topological dynamics <br />
of topological groups, i.e. the study of the continuous actions of a <br />
topological group on a compact space. We are particularly interested <br />
in the minimal actions, those for which every orbit is dense. <br />
The study of minimal actions is aided by a classical theorem of Ellis, <br />
who proved that for any topological group G, there exists a universal <br />
minimal flow (UMF), a minimal G-action which factors onto every other <br />
minimal G-action. Here, we will focus on two classes of groups: <br />
a countable discrete group and the automorphism group of a countable <br />
first-order structure. In the case of a countable discrete group, <br />
Baire category methods can be used to show that the collection of <br />
minimal flows is quite rich and that the UMF is rather complicated. <br />
For an automorphism group G of a countable structure, combinatorial <br />
methods can be used to show that sometimes, the UMF is trivial, or <br />
equivalently that every continuous action of G on a compact space <br />
admits a global fixed point.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18748Analysis Seminar2020-01-22T23:45:34Z<p>Seeger: /* Ruixiang Zhang */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18744Analysis Seminar2020-01-22T19:28:37Z<p>Seeger: /* Ruixiang Zhang */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the solution to this equation gets smoother when averaged over time. Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18743Analysis Seminar2020-01-22T19:28:03Z<p>Seeger: /* Ruixiang Zhang */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the solution to this equation gets smoother when averaged over time. Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions $2+1$. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18742Analysis Seminar2020-01-22T19:27:42Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions<br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the solution to this equation gets smoother when averaged over time. Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions $2+1$. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18741Analysis Seminar2020-01-22T19:27:24Z<p>Seeger: /* Abstracts */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local Smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions<br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the solution to this equation gets smoother when averaged over time. Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions $2+1$. A key ingredient in the proof is an incidence type theorem.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18739Analysis Seminar2020-01-22T19:21:53Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local Smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
n 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18738Analysis Seminar2020-01-22T19:19:41Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Title ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
n 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18635Analysis Seminar2020-01-15T04:34:02Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
n 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18634Analysis Seminar2020-01-15T04:24:42Z<p>Seeger: /* Abstracts */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
n 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18633Analysis Seminar2020-01-15T04:24:13Z<p>Seeger: /* Abstracts */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
n 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18632Analysis Seminar2020-01-15T04:23:07Z<p>Seeger: /* Abstracts */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
n 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, in particular to number theorists and analysts.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18631Analysis Seminar2020-01-15T04:15:46Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18630Analysis Seminar2020-01-15T04:14:25Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Speaker<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Host<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18613Analysis Seminar2020-01-10T17:17:02Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#Lillian Pierce | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Dmitry Chelkak<br />
| Ecole Normale, Paris<br />
|[[#linktoabstract | Title ]]<br />
| Denisov<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18612Analysis Seminar2020-01-10T17:15:15Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Friday, Jan 31, 3 pm, B119<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#Lillian Pierce | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Dmitry Chelkak<br />
| Ecole Normale, Paris<br />
|[[#linktoabstract | Title ]]<br />
| Denisov<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18398Analysis Seminar2019-11-11T21:20:27Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#linktoabstract | Title ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18257Analysis Seminar2019-10-27T19:48:05Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#linktoabstract | Title ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18071Analysis Seminar2019-10-01T18:58:35Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18070Analysis Seminar2019-10-01T18:57:27Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman (tent.)<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18060Analysis Seminar2019-10-01T13:31:29Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman (tent.)<br />
|University of Edinburgh<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=18059Analysis Seminar2019-10-01T13:28:25Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-|<br />
|Jonathan Hickman (tent.)<br />
|University of Edinburgh<br />
|May 5<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17662Analysis Seminar2019-08-21T11:32:40Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17623Colloquia2019-08-09T15:52:12Z<p>Seeger: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| Will Sawin (Columbia)<br />
|<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|Elchnanan Mossel (MIT) Distinguished Lecture<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|-<br />
|Oct 18<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Possibly reserved for job talk?<br />
|<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|<br />
|-<br />
|Jan 31<br />
|<br />
|-<br />
|Feb 7<br />
|<br />
|-<br />
|Feb 14<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 24<br />
|<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17614Colloquia2019-08-06T03:08:12Z<p>Seeger: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| <br />
|<br />
| <br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|Elchnanan Mossel (MIT) Distinguished Lecture<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|-<br />
|Oct 18<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Possibly reserved for job talk?<br />
|<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|<br />
|-<br />
|Jan 31<br />
|<br />
|-<br />
|Feb 7<br />
|<br />
|-<br />
|Feb 14<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Tent. reserved<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 24<br />
|<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17613Colloquia2019-08-06T02:55:04Z<p>Seeger: /* Spring 2020 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| <br />
|<br />
| <br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|Elchnanan Mossel (MIT) Distinguished Lecture<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|-<br />
|Oct 18<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Possibly reserved for job talk?<br />
|<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|<br />
|-<br />
|Jan 31<br />
|<br />
|-<br />
|Feb 7<br />
|<br />
|-<br />
|Feb 14<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|Tent. reserved<br />
|<br />
|Andreas<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 24<br />
|<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17610Colloquia2019-08-05T10:56:07Z<p>Seeger: /* Fall 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| tentatively reserved<br />
|<br />
| Betsy<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|Elchnanan Mossel (MIT) Distinguished Lecture<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|-<br />
|Oct 18<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Possibly reserved for job talk?<br />
|<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|<br />
|-<br />
|Jan 31<br />
|<br />
|-<br />
|Feb 7<br />
|<br />
|-<br />
|Feb 14<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 24<br />
|<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17608Colloquia2019-08-03T18:11:30Z<p>Seeger: /* Fall 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| tentatively reserved<br />
|<br />
| Betsy<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|Elchnanan Mossel (MIT) Distinguished Lecture<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|-<br />
|Oct 18<br />
|Tentatively reserved<br />
|<br />
|Andreas<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Possibly reserved for job talk?<br />
|<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|<br />
|-<br />
|Jan 31<br />
|<br />
|-<br />
|Feb 7<br />
|<br />
|-<br />
|Feb 14<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 24<br />
|<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Colloquia&diff=17607Colloquia2019-08-03T18:11:12Z<p>Seeger: /* Fall 2019 */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6<br />
| tentatively reserved<br />
|<br />
|<br />
| Betsy<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| Alicia Dickenstein (Buenos Aires)<br />
|[[# TBA| TBA ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| Jianfeng Lu (Duke)<br />
|[[#TBA | TBA]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 27<br />
|Elchnanan Mossel (MIT) Distinguished Lecture<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
|<br />
|-<br />
|Oct 18<br />
|Tentatively reserved<br />
|<br />
|Andreas<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Possibly reserved for job talk?<br />
|<br />
|-<br />
|Nov 8<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 15<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 22<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|<br />
|-<br />
|Jan 31<br />
|<br />
|-<br />
|Feb 7<br />
|<br />
|-<br />
|Feb 14<br />
|<br />
|-<br />
|Feb 21<br />
|<br />
|-<br />
|Feb 28<br />
|<br />
|-<br />
|March 6<br />
|<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 24<br />
|<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17591Analysis Seminar2019-07-30T01:35:36Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| tent. reserve<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17589Analysis Seminar2019-07-29T21:04:54Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| Uni Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| tent. reserve<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17587Analysis Seminar2019-07-29T12:37:20Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| Uni Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| tent. reserve<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| tent. reserve<br />
| <br />
|[[#linktoabstract | Title ]]<br />
| Andreaa<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17505Analysis Seminar2019-07-06T16:26:25Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 15<br />
| Bassam Shayya<br />
| American University of Beirut <br />
|[[#linktoabstract | Title ]]<br />
| Andreas, Betsy<br />
|-<br />
|Oct 22<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17504Analysis Seminar2019-07-06T13:26:44Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 15<br />
| Bassam Shayya<br />
| American University of Beirut <br />
|[[#linktoabstract | Title ]]<br />
| Andreas, Betsy<br />
|-<br />
|Oct 22<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17501Analysis Seminar2019-06-20T16:03:20Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 17<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 15<br />
| Bassam Shayya<br />
| American University of Beirut <br />
|[[#linktoabstract | Title ]]<br />
| Andreas, Betsy<br />
|-<br />
|Oct 22<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17495Analysis Seminar2019-06-06T21:46:40Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 17<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 15<br />
| Bassam Shayya<br />
| American University of Beirut <br />
|[[#linktoabstract | Title ]]<br />
| Andreas, Betsy<br />
|-<br />
|Oct 22<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seeger