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 Title
September 12 Title
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 Title Betsy
October 10 Michael Greenblatt UI Chicago Title Andreas
October 17 David Beltran Bilbao 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
November 14 Naser Talebizadeh Sardari UW Madison Title 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 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.


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Abstract


Naser Talebizadeh Sardari

Quadratic forms and the semiclassical eigenfunction hypothesis

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

Name

Title

Abstract

Extras

Blank Analysis Seminar Template