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−  '''Analysis Seminar
 
−  '''
 
   
−  The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.  +  The 20202021 Analysis Seminar will be organized by David Beltran and Andreas Seeger. 
 +  It will be online at least for the Fall semester, with details to be announced in September. 
 +  The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar earlier to accomodate speakers). 
   
−  If you wish to invite a speaker please contact Brian at street(at)math
 +  Zoom links will be sent to those who have signed up for the Analysis Seminar List. For instructions how to sign up for seminar lists, see https://www.math.wisc.edu/node/230 
   
−  ===[[Previous Analysis seminars]]===
 +  If you'd like to suggest speakers for the spring semester please contact David and Andreas (dbeltran at math, seeger at math). 
   
−  = Analysis Seminar Schedule =  +  
 +  
 +  =[[Previous_Analysis_seminars]]= 
 +  
 +  https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars 
 +  
 +  = Current Analysis Seminar Schedule = 
 { cellpadding="8"   { cellpadding="8" 
 !align="left"  date   !align="left"  date 
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 !align="left"  host(s)   !align="left"  host(s) 
     
−  Sept 11  +  September 22 
−   Simon Marshall  +  Alexei Poltoratski 
−   UW Madison  +  UW Madison 
−  [[#Simon Marshall  Integrals of eigenfunctions on hyperbolic manifolds ]]  +  [[#Alexei Poltoratski  Dirac inner functions ]] 
     
     
−  '''Wednesday, Sept 12'''  +  September 29 
−   Gunther Uhlmann  +  Polona Durcik 
−   University of Washington  +   Chapman University 
−   Distinguished Lecture Series  +  [[#linktoabstract  Title ]] 
−   See colloquium website for location  +   
     
−  '''Friday, Sept 14'''  +  September 30 
−   Gunther Uhlmann  +  Joris Roos 
−   University of Washington  +  University of Massachusetts  Lowell 
−   Distinguished Lecture Series  +  [[#linktoabstract  Title ]] 
−   See colloquium website for location  +   
     
−  Sept 18  +  October 6 
−   Grad Student Seminar  +  Andrew Zimmer 
 +  UW Madison 
 +  [[#linktoabstract  Title ]] 
     
−  
 
−  
 
     
−  Sept 25  +  October 13 
−   Grad Student Seminar  +  Hong Wang 
−    +  Princeton/IAS 
−    +  [[#linktoabstract  Title ]] 
−    +   
     
−  Oct 9  +  October 20 
−   Hong Wang  +  Kevin Luli 
−   MIT  +  UC Davis 
−  [[#Hong Wang  About Falconer distance problem in the plane ]]  +  [[#linktoabstract  Title ]] 
−   Ruixiang  +   
     
−  Oct 16  +  October 27 
−   Polona Durcik  +  Terence Harris 
−   Caltech  +   Cornell University 
−  [[#Polona Durcik  Singular BrascampLieb inequalities and extended boxes in R^n ]]
 +  [[#linktoabstract  Title ]] 
−   Joris
 
−  
 
−  Oct 23
 
−   SongYing Li
 
−   UC Irvine
 
−  [[#SongYing Li  Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudoHermitian manifold ]]
 
−   Xianghong
 
−  
 
−  Oct 30
 
−  Grad student seminar
 
−  
 
−  
 
−  
 
−  
 
−  Nov 6
 
−   Hanlong Fang
 
−   UW Madison
 
−  [[#Hanlong Fang  A generalization of the theorem of Weil and Kodaira on prescribing residues ]]
 
−   Brian
 
−  
 
−  '''Monday, Nov. 12, B139'''
 
−   Kyle Hambrook
 
−   San Jose State University
 
−  [[#Kyle Hambrook  Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]  
−   Andreas
 
−  
 
−  Nov 13
 
−   Laurent Stolovitch
 
−   Université de Nice  Sophia Antipolis
 
−  [[#Laurent Stolovitch  Equivalence of CauchyRiemann manifolds and multisummability theory ]]
 
−  Xianghong
 
−  
 
−  Nov 20
 
−   Grad Student Seminar
 
−  
 
−  [[#linktoabstract  ]]
 
     
     
−  Nov 27  +  Monday, November 2, 4 p.m. 
−   No Seminar  +  Yuval Wigderson 
−    +  Stanford University 
−  [[#linktoabstract  ]]  +  [[#linktoabstract  Title ]] 
     
     
−  Dec 4  +  November 10 
−   No Seminar  +  Óscar Domínguez 
−  [[#linktoabstract  ]]  +   Universidad Complutense de Madrid 
 +  [[#linktoabstract  Title ]] 
     
     
−  Jan 22  +  November 17 
−   Brian Cook  +  Tamas Titkos 
−   Kent  +  BBS U of Applied Sciences and Renyi Institute 
−  [[#Brian Cook  Equidistribution results for integral points on affine homogenous algebraic varieties ]]  +  [[#linktoabstract  Title ]] 
−   Street
 
−  
 
−  Jan 29
 
−   No Seminar
 
     
−  [[#linktoabstract  ]]
 
−  
 
     
−  Feb 5, '''B239'''  +  November 24 
−   Alexei Poltoratski  +  Shukun Wu 
−   Texas A&M  +  University of Illinois (UrbanaChampaign) 
−  [[#Alexei Poltoratski  Completeness of exponentials: BeurlingMalliavin and type problems ]]
 +  [[#linktoabstract  Title ]] 
−   Denisov  
−  
 
−  '''Friday, Feb 8'''
 
−   Aaron Naber
 
−   Northwestern University
 
−  [[#linktoabstract  A structure theory for spaces with lower Ricci curvature bounds ]]  
−   See colloquium website for location
 
−  
 
−  Feb 12
 
−   Shaoming Guo
 
−   UW Madison
 
−  [[#Shaoming Guo  Polynomial Roth theorems in Salem sets ]]
 
     
     
−  '''Wed, Feb 13, B239'''  +  December 1 
−   Dean Baskin  +   Jonathan Hickman 
−   TAMU  +   The University of Edinburgh 
−  [[# Dean Baskin  Radiation fields for wave equations ]]
 +  [[#linktoabstract  Title ]] 
−   Colloquium
 
−  
 
−  '''Friday, Feb 15'''
 
−   Lillian Pierce
 
−   Duke
 
−  [[#Lillian Pierce  Short character sums ]]
 
−   Colloquium
 
−  
 
−  '''Monday, Feb 18, 3:30 p.m, B239.'''
 
−   Daniel Tataru
 
−   UC Berkeley
 
−  [[#Daniel Tataru  A Morawetz inequality for water waves ]]
 
−   PDE Seminar
 
−  
 
−  Feb 19
 
−   Wenjia Jing
 
−  Tsinghua University
 
−  Periodic homogenization of Dirichlet problems in perforated domains: a unified proof
 
−   PDE Seminar
 
−  
 
−  Feb 26
 
−   No Seminar
 
−  
 
−  
 
−  
 
−  Mar 5
 
−   Loredana Lanzani
 
−   Syracuse University
 
−  [[#Loredana Lanzani  On regularity and irregularity of the CauchySzegő projection in several complex variables ]]  
−   Xianghong
 
−  
 
−  Mar 12
 
−   Trevor Leslie
 
−   UW Madison
 
−  [[#Trevor Leslie  Energy Equality for the NavierStokes Equations at the First Possible Blowup Time ]]
 
−  
 
−  
 
−  Mar 19
 
−  Spring Break!
 
     
−  
 
−  
 
     
−  Mar 26  +  December 8 
−   No seminar  +  TBA 
     
−  [[#linktoabstract  ]]  +  [[#linktoabstract  Title ]] 
     
     
−  Apr 2  +  February 2 
−   Stefan Steinerberger  +  Jongchon Kim 
−   Yale  +   UBC 
−  [[#Stefan Steinerberger  Wasserstein Distance as a Tool in Analysis ]]  +  [[#linktoabstract  Title ]] 
−   Shaoming, Andreas  +   
     
−   +  February 9 
−  Apr 9  +  Bingyang Hu 
−   Franc Forstnerič  +  Purdue University 
−   Unversity of Ljubljana
 +  [[#linktoabstract  Title ]] 
−  [[#Franc Forstnerič  Minimal surfaces by way of complex analysis ]]
 +   
−   Xianghong, Andreas
 
−  
 
−  Apr 16
 
−   Andrew Zimmer
 
−   Louisiana State University
 
−  [[#Andrew Zimmer  The geometry of domains with negatively pinched Kaehler metrics ]]
 
−   Xianghong
 
−  
 
−  Apr 23
 
−   Brian Street
 
−   University of WisconsinMadison  
−  [[#Brian Street  Maximal Hypoellipticity ]]  
−   Street  
−  
 
−  Apr 30
 
−   Zhen Zeng
 
−   UPenn
 
−  [[#Zhen Zeng  Decay property of multilinear oscillatory integrals ]]
 
−   Shaoming
 
−  
 
−  Summer
 
−  
 
−  September 10
 
−  Jose Madrid
 
−  UCLA
 
−  
 
−  Andreas, David
 
     
 +  February 16 
 +  David Beltran 
 +  UW  Madison 
 +  [[#linktoabstract  Title ]] 
 +  } 
   
 =Abstracts=   =Abstracts= 
−  ===Simon Marshall===
 
− 
 
−  ''Integrals of eigenfunctions on hyperbolic manifolds''
 
− 
 
−  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.
 
− 
 
− 
 
−  ===Hong Wang===
 
− 
 
−  ''About Falconer distance problem in the plane''
 
− 
 
−  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.
 
− 
 
−  ===Polona Durcik===
 
− 
 
−  ''Singular BrascampLieb inequalities and extended boxes in R^n''
 
− 
 
−  BrascampLieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular BrascampLieb inequalities, which arise when one of the functions is replaced by a CalderonZygmund 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.
 
− 
 
− 
 
−  ===SongYing Li===
 
− 
 
−  ''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudoHermitian manifold''
 
− 
 
−  In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates
 
−  for the first positive eigenvalues of Kohn Laplacian and subLaplacian on a strictly pseudoconvex pseudoHermitian CR manifold,
 
−  which include CR LichnerowiczObata theorem for the lower and upper bounds for the first positive eigenvalue for the
 
−  Kohn Laplacian on strictly pseudoconvex hypersurfaces.
 
− 
 
− 
 
−  ===Hanlong Fan===
 
− 
 
−  ''A generalization of the theorem of Weil and Kodaira on prescribing residues''
 
− 
 
−  An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic oneform 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 nonK\"ahler manifolds.
 
− 
 
−  ===Kyle Hambrook===
 
− 
 
−  ''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''
 
− 
 
−  I will discuss my recent work on some problems concerning
 
−  Fourier decay and Fourier restriction for fractal measures on curves.
 
− 
 
−  ===Laurent Stolovitch===
 
− 
 
−  ''Equivalence of CauchyRiemann manifolds and multisummability theory''
 
− 
 
−  We apply the multisummability theory from Dynamical Systems to CRgeometry. As the main result, we show that two realanalytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CRequivalent at the respective point. As a corollary, we prove that all formal equivalences between realalgebraic Levinonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.
 
− 
 
− 
 
−  ===Brian Cook===
 
− 
 
−  ''Equidistribution results for integral points on affine homogenous algebraic varieties''
 
− 
 
−  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.
 
− 
 
 ===Alexei Poltoratski===   ===Alexei Poltoratski=== 
   
−  ''Completeness of exponentials: BeurlingMalliavin and type problems''
 +  Title: Dirac inner functions 
   
−  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^2space. The BerulingMalliavin 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.
 +  Abstract: My talk will focus on some new (and old) complex analytic objects arising from Dirac systems of differential equations. 
 +  We will discuss connections between problems in complex function theory, spectral and scattering problems for differential 
 +  operators and the nonlinear Fourier transform. 
   
   
−  ===Shaoming Guo===  +  ===Name=== 
   
−  ''Polynomial Roth theorems in Salem sets''
 +  Title 
   
−  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.
 +  Abstract 
   
   
 +  ===Name=== 
   
 +  Title 
   
−  ===Dean Baskin===
 +  Abstract 
   
−  ''Radiation fields for wave equations''
 
   
−  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.
 +  ===Name=== 
   
−  ===Lillian Pierce===
 +  Title 
   
−  ''Short character sums''
 +  Abstract 
   
−  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 socalled character sum. For example, both understanding the Riemann zeta function or Dirichlet Lfunctions 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.
 
   
−  ===Loredana Lanzani===  +  ===Name=== 
   
−  ''On regularity and irregularity of the CauchySzegő projection in several complex variables''
 +  Title 
   
−  This talk is a survey of my latest, and now final, collaboration with Eli Stein.
 +  Abstract 
   
−  It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudoconvex, the CauchySzegő 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 pseudoconvex. Our starting point are the ideas of KiselmanBarrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the CauchySzegő 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 CauchyLeray integral, where however the relevant counterexample is of much simpler nature.
 +  =Extras= 
−   +  [[Blank Analysis Seminar Template]] 
−  ===Trevor Leslie===  
−   
−  ''Energy Equality for the NavierStokes Equations at the First Possible Blowup Time''
 
−   
−  In this talk, we discuss the problem of energy equality for strong solutions of the NavierStokes 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).
 
   
−  ===Stefan Steinerberger===
 
   
−  ''Wasserstein Distance as a Tool in Analysis''
 +  Graduate Student Seminar: 
   
−  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 realvalued 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 codimension 1 (this is already interesting for trigonometric polynomials on the 2torus, 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.
 +  https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html 
−   
−  ===Franc Forstnerič===
 
−   
−  ''Minimal surfaces by way of complex analysis''
 
−   
−  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 CalabiYau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.
 
−   
−  ===Andrew Zimmer===
 
−   
−  ''The geometry of domains with negatively pinched Kaehler metrics''
 
−   
−  Every bounded pseudoconvex domain in C^n has a natural complete metric: the KaehlerEinstein metric constructed by ChengYau. When the boundary of the domain is strongly pseudoconvex, ChengYau 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.
 
−   
−   
−  ===Brian Street===
 
−   
−  ''Maximal Hypoellipticity''
 
−   
−  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.
 
−   
−   
−  ===Zhen Zeng===
 
−   
−  ''Decay property of multilinear oscillatory integrals''
 
−   
−  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
 
−  \[
 
−  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,
 
−  \]
 
−  which falls into the broad goal in the previous work of Christ, Li, Tao and Thiele.
 
−   
−  =Extras=
 
−  [[Blank Analysis Seminar Template]]
 