Analysis Seminar

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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

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 multi-layered 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 two-dimensional hypersurfaces Andreas
October 17 David Beltran Basque Center of Applied Mathematics Fefferman-Stein 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


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 sub-Riemannian 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 "sub-Hermitian".

Hiroyoshi Mitake

Title: Derivation of multi-layered interface system and its application

Abstract: In this talk, I will propose a multi-layered interface system which can be formally derived by the singular limit of the weakly coupled system of the Allen-Cahn equation. By using the level set approach, this system can be written as a quasi-monotone degenerate parabolic system. We give results of the well-posedness 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 two-weighted 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 Fefferman-Stein inequalities for pseudodifferential operators and for the solution operators to dispersive equations.

Naser Talebizadeh Sardari

Quadratic forms and the semiclassical eigenfunction hypothesis

Let [math]Q(X)[/math] be any integral primitive positive definite quadratic form in [math]k[/math] variables, where [math]k\geq4[/math], and discriminant [math]D[/math]. For any integer [math]n[/math], we give an upper bound on the number of integral solutions of [math]Q(X)=n[/math] in terms of [math]n[/math], [math]k[/math], and [math]D[/math]. 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 [math]\mathbb{T}^d[/math] for [math]d\geq 5[/math]. This conjecture is motivated by the work of Berry\cite{Berry, Michael} on semiclassical eigenfunction hypothesis.





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