https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Seeger&feedformat=atomUW-Math Wiki - User contributions [en]2019-12-05T21:55:33ZUser contributionsMediaWiki 1.30.1https://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>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17477Analysis Seminar2019-06-01T23:36:29Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|*[https://www.math.wisc.edu/seeger2019/?q=node/2 Madison Lectures in Fourier Analysis]<br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|-<br />
|Oct 15<br />
|Bassam Shayya<br />
|American University of Beirut<br />
|<br />
|Andreas, Betsy<br />
<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17476Analysis Seminar2019-06-01T23:35:18Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|[https://www.math.wisc.edu/seeger2019/?q=node/2.html Madison Lectures in Fourier Analysis]<br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|-<br />
|Oct 15<br />
|Bassam Shayya<br />
|American University of Beirut<br />
|<br />
|Andreas, Betsy<br />
<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17475Analysis Seminar2019-06-01T23:30:21Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|May 17-23<br />
|*[https://www.math.wisc.edu/seeger2019/?q=node/2.html Madison Lectures in Fourier Analysis]<br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17474Analysis Seminar2019-06-01T23:29:18Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|May 17-23<br />
|*[http://www.math.wisc.edu/~seeger/spring14.html Spring 2014]<br />
|*[https://www.math.wisc.edu/seeger2019/?q=node/2.html Madison Lectures in Fourier Analysis]<br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17473Analysis Seminar2019-06-01T23:28:26Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|May 17-23<br />
|*[http://www.math.wisc.edu/~seeger/spring14.html Spring 2014]<br />
|*[a href=https://www.math.wisc.edu/seeger2019/?q=node/2 Madison Lectures in Fourier Analysis]<br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17472Analysis Seminar2019-06-01T23:28:01Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|May 17-23<br />
|*[http://www.math.wisc.edu/~seeger/spring14.html Spring 2014]<br />
|[*a href=https://www.math.wisc.edu/seeger2019/?q=node/2 Madison Lectures in Fourier Analysis]<br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17471Analysis Seminar2019-06-01T23:25:21Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|May 17-23<br />
|*[http://www.math.wisc.edu/~seeger/spring14.html Spring 2014]<br />
|<a href=https://www.math.wisc.edu/seeger2019/?q=node/2> Madison Lectures in Fourier Analysis</a><br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17470Analysis Seminar2019-06-01T23:22:38Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|May 17-23<br />
|<a href=https://www.math.wisc.edu/seeger2019/?q=node/2> Madison Lectures in Fourier Analysis</a><br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17469Analysis Seminar2019-06-01T23:21:52Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|May 17-23<br />
|<a href="https://www.math.wisc.edu/seeger2019/?q=node/2"> Madison Lectures in Fourier Analysis</a><br />
|-<br />
|Summer<br />
|-<br />
|Sept 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17468Analysis Seminar2019-06-01T23:15:33Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|Summer<br />
|-<br />
|September 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17467Analysis Seminar2019-06-01T23:15:07Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|Summer<br />
|-<br />
|September 10<br />
|Jose Madrid<br />
|UCLA<br />
|<br />
|Andreas, David<br />
|-<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17466Analysis Seminar2019-06-01T23:13:07Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#Brian Street | Maximal Hypoellipticity ]]<br />
| Street<br />
|-<br />
|Apr 30<br />
| Zhen Zeng<br />
| UPenn<br />
|[[#Zhen Zeng | Decay property of multilinear oscillatory integrals ]]<br />
| Shaoming<br />
|-<br />
|Summer<br />
|-<br />
|Jose Madrid<br />
|<br />
|-<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
===Brian Street===<br />
<br />
''Maximal Hypoellipticity''<br />
<br />
In 1974, Folland and Stein introduced a generalization of ellipticity known as maximal hypoellipticity. This talk will be an introduction to this concept and some of the ways it generalizes ellipticity.<br />
<br />
<br />
===Zhen Zeng===<br />
<br />
''Decay property of multilinear oscillatory integrals''<br />
<br />
In this talk, I will be talking about the conditions of the phase function $P$ and the linear mappings $\{\pi_i\}_{i=1}^n$ to ensure the asymptotic power decay properties of the following trilinear oscillatory integrals <br />
\[<br />
I_{\lambda}(f_1,f_2,f_3)=\int_{\mathbb{R}^m}e^{i\lambda P(x)}\prod_{j=1}^3 f_j(\pi_j(x))\eta(x)dx, <br />
\]<br />
which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17206Analysis Seminar2019-03-24T17:55:58Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17205Analysis Seminar2019-03-24T17:54:24Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17204Analysis Seminar2019-03-24T00:27:37Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger t | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17203Analysis Seminar2019-03-24T00:24:17Z<p>Seeger: /* Abstracts */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[# Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger t | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17202Analysis Seminar2019-03-24T00:23:52Z<p>Seeger: /* Abstracts */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[# Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger t | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
+++Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17201Analysis Seminar2019-03-24T00:22:13Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[# Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger t | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17198Analysis Seminar2019-03-23T00:40:10Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[# Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17197Analysis Seminar2019-03-23T00:39:31Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[# Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17173Analysis Seminar2019-03-15T22:33:15Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[# Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17139Analysis Seminar2019-03-11T21:00:27Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[# Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17116Analysis Seminar2019-03-06T08:38:39Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17115Analysis Seminar2019-03-06T08:38:02Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| <br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=17111Analysis Seminar2019-03-05T19:12:07Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[# Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=16978Analysis Seminar2019-02-18T11:25:19Z<p>Seeger: /* Abstracts */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=16977Analysis Seminar2019-02-18T11:24:15Z<p>Seeger: /* Abstracts */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=16976Analysis Seminar2019-02-18T11:21:35Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=16975Analysis Seminar2019-02-18T11:21:15Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seegerhttps://www.math.wisc.edu/wiki/index.php?title=Analysis_Seminar&diff=16974Analysis Seminar2019-02-18T11:20:18Z<p>Seeger: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Analysis Seminar<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 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[# Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#lDaniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!!!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Seeger