Analysis Seminar
Analysis Seminar
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.
If you wish to invite a speaker please contact Betsy at stovall(at)math
Contents
Previous Analysis seminars
Summer/Fall 2017 Analysis Seminar Schedule
date  speaker  institution  title  host(s) 

September 8 in B239  Tess Anderson  UW Madison  A Spherical Maximal Function along the Primes  Tonghai 
September 19  Brian Street  UW Madison  Convenient Coordinates  Betsy 
September 26  Hiroyoshi Mitake  Hiroshima University  Derivation of multilayered interface system and its application  Hung 
October 3  Joris Roos  UW Madison  A polynomial Roth theorem on the real line  Betsy 
October 10  Michael Greenblatt  UI Chicago  Maximal averages and Radon transforms for twodimensional hypersurfaces

Andreas 
October 17  David Beltran  Basque Center of Applied Mathematics  FeffermanStein inequalities  Andreas 
Wednesday, October 18 in B131  Jonathan Hickman  University of Chicago  Title  Andreas 
October 24  Xiaochun Li  UIUC  Title  Betsy 
Thursday, October 26  Fedya Nazarov  Kent State University  Title  Betsy, Andreas 
Friday, October 27 in B239  Stefanie Petermichl  University of Toulouse  Title  Betsy, Andreas 
Wednesday, November 1 in B239  Shaoming Guo  Indiana University  Title  Andreas 
November 14  Naser Talebizadeh Sardari  UW Madison  Quadratic forms and the semiclassical eigenfunction hypothesis  Betsy 
November 28  Xianghong Chen  UW Milwaukee  Title  Betsy 
December 5  Title  
December 12  Alex Stokolos  GA Southern  Title  Andreas 
Abstracts
Brian Street
Title: Convenient Coordinates
Abstract: We discuss the method of picking a convenient coordinate system adapted to vector fields. Let X_1,...,X_q be either real or complex C^1 vector fields. We discuss the question of when there is a coordinate system in which the vector fields are smoother (e.g., C^m, or C^\infty, or real analytic). By answering this in a quantitative way, we obtain coordinate charts which can be used as generalized scaling maps. When the vector fields are real this is joint work with Stovall, and continues in the line of quantitative subRiemannian geometry initiated by Nagel, Stein, and Wainger. When the vector fields are complex one obtains a geometry with more structure which can be thought of as "subHermitian".
Hiroyoshi Mitake
Title: Derivation of multilayered interface system and its application
Abstract: In this talk, I will propose a multilayered interface system which can be formally derived by the singular limit of the weakly coupled system of the AllenCahn equation. By using the level set approach, this system can be written as a quasimonotone degenerate parabolic system. We give results of the wellposedness of viscosity solutions, and study the singularity of each layers. This is a joint work with H. Ninomiya, K. Todoroki.
Joris Roos
Title: A polynomial Roth theorem on the real line
Abstract: For a polynomial P of degree greater than one, we show the existence of patterns of the form (x,x+t,x+P(t)) with a gap estimate on t in positive density subsets of the reals. This is an extension of an earlier result of Bourgain. Our proof is a combination of Bourgain’s approach and more recent methods that were originally developed for the study of the bilinear Hilbert transform along curves. This talk is based on a joint work with Polona Durcik and Shaoming Guo.
David Beltran
Fefferman Stein Inequalities
Given an operator T, we focus on obtaining twoweighted inequalities in which the weights are related via certain maximal function. These inequalites, which originated in work of Fefferman and Stein, have been established in an optimal way for different classical operators in Harmonic Analysis. In this talk, we survey some classical results and we present some recent FeffermanStein inequalities for pseudodifferential operators and for the solution operators to dispersive equations.
Naser Talebizadeh Sardari
Quadratic forms and the semiclassical eigenfunction hypothesis
Let be any integral primitive positive definite quadratic form in variables, where , and discriminant . For any integer , we give an upper bound on the number of integral solutions of in terms of , , and . As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus for . This conjecture is motivated by the work of Berry\cite{Berry, Michael} on semiclassical eigenfunction hypothesis.
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