https://www.math.wisc.edu/wiki/index.php?title=Special:NewPages&feed=atom&hideredirs=1&limit=50&offset=&namespace=0&username=&tagfilter=&size-mode=max&size=0UW-Math Wiki - New pages [en]2020-08-13T15:45:03ZFrom UW-Math WikiMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php/Dynamics_Seminar_2020-2021Dynamics Seminar 2020-20212020-08-10T17:38:16Z<p>Dymarz: </p>
<hr />
<div>The [[Dynamics Seminar]] meets virutal on '''Wednesdays''' from '''2:30pm - 3:20pm'''.<br />
<br> <br />
For more information, contact Chenxi Wu.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Fall 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 16<br />
|Andrew Zimmer (Wisconsin)<br />
|TBA<br />
| (local)<br />
|-<br />
|September 23<br />
|Andrew Zimmer (Wisconsin)<br />
|TBA<br />
| (local)<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Andrew Zimmer===<br />
<br />
"TBA"</div>Dymarzhttps://www.math.wisc.edu/wiki/index.php/Fall_2019_and_Spring_2020_Analysis_SeminarsFall 2019 and Spring 2020 Analysis Seminars2020-08-03T20:33:48Z<p>Nagreen: Created page with "'''Fall 2019 and Spring 2020 Analysis Seminar Series ''' The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated. If you wish to invite a speaker p..."</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 />
|Nov 17, 2020<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|<br />
| Brian<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).</div>Nagreenhttps://www.math.wisc.edu/wiki/index.php/Applied/ACMS/absF20Applied/ACMS/absF202020-08-03T17:53:05Z<p>Jeanluc: Created page with "= ACMS Abstracts: Fall 2020 = === Nick Ouellette (Stanford) === Title: Tensor Geometry in the Turbulent Cascade Abstract: Perhaps the defining characteristic of turbulent f..."</p>
<hr />
<div>= ACMS Abstracts: Fall 2020 =<br />
<br />
=== Nick Ouellette (Stanford) ===<br />
<br />
Title: Tensor Geometry in the Turbulent Cascade<br />
<br />
Abstract: Perhaps the defining characteristic of turbulent flows is the directed flux of energy from the scales at which it is injected into the flow to the scales at which it is dissipated. Often, we think about this transfer of energy in a Fourier sense; but in doing so, we obscure its mechanistic origins and lose any connection to the spatial structure of the flow field. Alternatively, quite a bit of work has been done to try to tie the cascade process to flow structures; but such approaches lead to results that seem to be at odds with observations. Here, I will discuss what we can learn from a different way of thinking about the cascade, this time as a purely mechanical process where some scales do work on others and thereby transfer energy. This interpretation highlights the fundamental importance of the geometric alignment between the turbulent stress tensor and the scale-local rate of strain tensor, since if they are misaligned with each other, no work can be done and no energy will be transferred. We find that (perhaps surprisingly) these two tensors are in general quite poorly aligned, making the cascade a highly inefficient process. Our analysis indicates that although some aspects of this tensor alignment are dynamical, the quadratic nature of Navier-Stokes nonlinearity and the embedding dimension provide significant constraints, with potential implications for turbulence modeling.</div>Jeanluchttps://www.math.wisc.edu/wiki/index.php/Applied/ACMS/Spring2021Applied/ACMS/Spring20212020-06-08T15:35:53Z<p>Spagnolie: Created page with "== Spring 2021 == {| cellpadding="8" !align="left" | date !align="left" | speaker !align="left" | title !align="left" | host(s) |- | Jan 29 | | | |- | Feb 5 | | | |- | Feb..."</p>
<hr />
<div>== Spring 2021 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| Jan 29<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 5<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 12<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 19<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 26<br />
|<br />
|<br />
|<br />
|-<br />
| Mar 5<br />
|<br />
|<br />
|<br />
|-<br />
| Mar 12<br />
|<br />
|<br />
|<br />
|-<br />
| Mar 19<br />
|<br />
|<br />
|<br />
|-<br />
| Mar 26<br />
|(spring break)<br />
|<br />
|<br />
|-<br />
| Apr 2<br />
|<br />
|<br />
|<br />
|-<br />
| Apr 9<br />
|<br />
|<br />
|<br />
|-<br />
| Apr 16<br />
|<br />
|<br />
|<br />
|-<br />
| Apr 23<br />
|<br />
|<br />
|<br />
|-<br />
|}</div>Spagnoliehttps://www.math.wisc.edu/wiki/index.php/Applied/Physical_Applied_Math/Spring2020Applied/Physical Applied Math/Spring20202020-05-20T14:50:55Z<p>Jeanluc: Created page with "== Spring 2020 == {| cellpadding="8" !align="left" | date !align="left" | speaker !align="left" | title |- |Jan. 30 |Jean-Luc |Organizational meeting; [https://www.dropbox...."</p>
<hr />
<div>== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan. 30<br />
|Jean-Luc<br />
|Organizational meeting; [https://www.dropbox.com/s/bnjpyud6h8u3lav/homog_periodic_lattice_group_meeting.pdf?dl=0 Homogenization of a periodic lattice]<br />
|-<br />
|Feb. 6<br />
|Gage<br />
|Krasilov et al., [https://bura.brunel.ac.uk/bitstream/2438/419/1/Growing%20Random%20Sequences.pdf Growing random sequences]<br> Makover and McGowan, [https://arxiv.org/abs/math/0510159 An elementary proof that random Fibonacci sequences grow exponentially]<br />
|-<br />
|Feb. 13<br />
|<br />
|''Faculty Meeting''<br />
|-<br />
|Feb. 20<br />
|Saverio<br />
|Greengard and Jiang, [https://epubs.siam.org/doi/abs/10.1137/18M1216158 A New Mixed Potential Representation for Unsteady, Incompressible Flow]<br />
|-<br />
|Feb. 27<br />
|<br />
|''Faculty (EC) Meeting''<br />
|-<br />
|Mar. 5<br />
|Wil<br />
|[https://www.dropbox.com/s/fbidvoslu3twtlv/pam_2020.pdf?dl=0 Implicit surfaces and the closest point problem]<br />
|-<br />
|Mar. 12<br />
|''cancelled''<br />
|<br />
|-<br />
|Mar. 19<br />
|Saverio<br />
|[https://www.dropbox.com/s/h9rmglss07bmyb6/BonusLecture.pdf?dl=0 Primer on SIR models and the epidemic]<br />
|-<br />
|Mar. 26 ''3:30pm''<br />
|Jean-Luc<br />
|[https://youtu.be/B0GNtFApUQ8 Shape Matters: Homogenization for a confined Brownian microswimmer] (seminar at Princeton)<br />
|-<br />
|Apr. 2<br />
|<br />
|''Faculty Meeting''<br />
|-<br />
|Apr. 9<br />
|Ruifu<br />
|Texier, [https://arxiv.org/abs/1907.08512 Fluctuations of the product of random matrices and generalised Lyapunov exponent] [https://www.dropbox.com/s/xb0jb833xzpmtdj/Ruifi_group_meeting.pdf?dl=0 notes]<br />
|-<br />
|Apr. 16<br />
|Jean-Luc<br />
|[https://www.dropbox.com/s/u66adsybjai7j5k/dumbbell_fluct.pdf Fluctuating dumbbell swimmer]<br />
|-<br />
|Apr. 23<br />
|Son<br />
|Allaire, [https://epubs.siam.org/doi/pdf/10.1137/0523084 Homogenization and Two-Scale Convergence]<br />
|-<br />
|}</div>Jeanluchttps://www.math.wisc.edu/wiki/index.php/Named_optionsNamed options2020-05-18T18:41:41Z<p>Hanhart: </p>
<hr />
<div>The '''Mathematics Major''' offers a variety of '''Named Options''' which allow a major to focus on those topics in mathematics which have a strong relationship to another area of study. This page describes those options and highlights topics and courses worthy of special consideration.<br />
<br />
<br />
<br />
== General Requirements and Notes for all Named Options ==<br />
In general, all named option programs will have the following requirements:<br />
<br />
1) A course in linear algebra (MATH 320, 340, 341, or 375).<br />
<br />
2) An intermediate level "transition" course or sequence: MATH 321/2, 341, 375, 421, or 467.<br />
<br />
3) A minimum of two advanced MATH courses (Numbered 500 and above).<br />
<br />
4) A minimum of 18 credits in MATH from no fewer than six courses above the 300 level.<br />
<br />
Any additional course/credit/level requirements are specific to each Named Option and students should refer to the '''[https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-bs/#requirementstext guide]''' for complete descriptions. <br />
<br />
NOTES:<br />
<br />
1) Be aware that the information below describes initial collections of courses and ideas worth considering which fulfill major requirements. '''Please refer to the '''[https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-bs/#requirementstext guide]'''for all possible courses which can be applied to your named option plan and meet with an advisor in order to construct a course plan which works best for you.'''<br />
<br />
2) Note that course suggestions '''may have prerequisites'''.<br />
<br />
3) Courses offered by departments/schools besides mathematics may have '''restricted enrollment'''.<br />
<br />
== MATHEMATICS FOR DATA, STATISTICS, AND RISK ANALYSIS ==<br />
For students interested in mathematics inspired by or used in the fields of Statistics, Data Science, Actuarial Science, Bio-Statistics, and many others.<br />
<br />
Students interested in this option should choose coursework focused on linear algebra, probability, statistics, analysis, and computational mathematics.<br />
<br />
The precise description of the requirements of this named option is available in the [https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-ba/mathematics-mathematics-data-risk-analysis-ba/#requirementstext guide].<br />
<br />
If you are interested in this option then please meet with a math faculty advisor in order to construct a course plan which works best for you.<br />
<br />
''Linear Algebra'':<br />
MATH 320, 340, 341, 375, 540<br />
<br />
''Probability'':<br />
MATH 309, 431, 531, 535<br />
<br />
''Statistics'':<br />
MATH 310<br />
<br />
''Analysis'':<br />
MATH 321 and 322, 421, 521<br />
<br />
''Numerical Methods'':<br />
MATH 514<br />
<br />
''Data/Risk/Stat Core'':<br />
ACT SCI 303 or <br />
(STAT 333 and STAT 424) or<br />
(STAT 340 and STAT 424)<br />
<br />
== MATHEMATICS FOR THE PHYSICAL AND BIOLOGICAL SCIENCES ==<br />
Mathematics and the natural sciences have had a long and fruitful relationship since the dawn of humanity. This named option may be of interest to any mathematics student with a strong interest in physics, chemistry, biology, and most areas of engineering.<br />
<br />
The precise description of the requirements of this named option is available in the [https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-ba/mathematics-mathematics-physical-biological-sciences-ba/#requirementstext guide].<br />
<br />
If you are interested in this option then please meet with a math faculty advisor in order to construct a course plan which works best for you.<br />
<br />
Students interested in this named option should focus on linear algebra, differential equations, geometry, and analysis.<br />
<br />
''Linear Algebra and Algebra'':<br />
MATH 320, 340, 341, 375, 540, 541<br />
<br />
''Differential Equations'':<br />
MATH 319, 320, 376, 519, 619<br />
<br />
''Geometry and Topology'':<br />
MATH 551, 561<br />
<br />
''Real and Complex Analysis'':<br />
MATH 321 and 322, 421, 514, 521, 623<br />
<br />
''Other topics'':<br />
MATH 531<br />
<br />
''Core Natural Science'':<br />
Physics 247/207/201/EMA 201 and Physics 248/208/202<br />
<br />
== MATHEMATICS FOR SECONDARY EDUCATION ==<br />
<br />
This option is designed with input from our own School of Education to cover all core areas of mathematics expected of a secondary instructor in the context of a mathematics major.<br />
<br />
The precise description of the requirements of this named option is available in the [https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-ba/mathematics-mathematics-secondary-education-ba/ guide].<br />
<br />
If you are interested in this option then please meet with a math faculty advisor in order to construct a course plan which works best for you.<br />
<br />
<br />
<br />
''Linear Algebra'': <br />
MATH 320, 340, 341, 375<br />
<br />
''Analysis'': MATH 421, 521<br />
<br />
''Algebra'':<br />
MATH 540, 541<br />
<br />
''Probability/Combinatorics'':<br />
MATH 309, 431, 475, 531<br />
<br />
''Statistics'':<br />
STAT 301, 302, 312, 324, MATH 310, ECON 310<br />
<br />
''History of Mathematics'':<br />
MATH 473<br />
<br />
''Geometry'':<br />
MATH 461<br />
<br />
''Capstone'':<br />
MATH 471<br />
<br />
== MATHEMATICS FOR ECONOMICS AND FINANCE ==<br />
This option is inspired by interesting problems and applications in certain areas of business and economics (operations management, financial modeling, market behavior, and so on).<br />
<br />
The mathematics is built around analysis, which allows us to link together different mathematical areas. For example: the theory of differential equations, which we use to model systems in order to make specific predictions on outcomes, with the theory of probability, which we use to model systems which have a variety of unknown outcomes. In addition to these topics, we recommend a strong background in linear algebra.<br />
<br />
The precise description of the requirements of this named option is available in the [https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-ba/mathematics-mathematics-economics-finance-ba/#requirementstext guide].<br />
<br />
If you are interested in this option then please meet with a math faculty advisor in order to construct a course plan which works best for you.<br />
<br />
<br />
<br />
''Linear Algebra'':<br />
MATH 320, 340, 341, 375, 443, 540<br />
<br />
''Differential Equations'': MATH 319, 320, 376, 415<br />
<br />
''Probability and Statistics'': MATH 309, 431, 310, 531<br />
<br />
''Analysis'':<br />
MATH 321-2 sequence, 421, 521(this is a required class for this program).<br />
<br />
''Introductory Econ/Finance Sequences'':<br />
Micro (ECON 301 or 311) and Macroeconomics (ECON 302 or 312) <br />
<br />
or<br />
<br />
FIN 300 and 320<br />
<br />
== MATHEMATICS FOR PROGRAMMING AND COMPUTING ==<br />
The areas of mathematics of interest here are often grouped as "discrete" and include topics in algebra, probability, and number theory. However, analysis plays an extremely strong role in unexpected ways. For example: An iterative system which builds successive approximations can be thought of as a sequence. So questions about how well that system works can be restated as questions about if the sequence has a limit, how quickly the sequence converges to that limit, and so on.<br />
<br />
The precise description of the requirements of this named option is available in the [https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-ba/mathematics-mathematics-programming-computing-ba/#requirementstext guide].<br />
<br />
If you are interested in this option then please meet with a math faculty advisor in order to construct a course plan which works best for you.<br />
<br />
''Algebra'': MATH 320, 340, 341, 375, 540, 541<br />
<br />
''Analysis'': MATH 321-2, 421, 514, 521<br />
<br />
''Probability'': MATH 309, 431, 531, 535<br />
<br />
'' Number Theory'': MATH 467, 567<br />
<br />
Other areas of interest include combinatorics (MATH 475) and logic (MATH 571).<br />
<br />
Students should also aim to complete the standard introductory programming sequence: CS 300 and 400.</div>Hanhart