Fall 2021 and Spring 2022 Analysis Seminars
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 | Title | 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".
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Naser Talebizadeh Sardari
Quadratic forms and the semiclassical eigenfunction hypothesis
Let [math]\displaystyle{ Q(X) }[/math] be any integral primitive positive definite quadratic form in [math]\displaystyle{ k }[/math] variables, where [math]\displaystyle{ k\geq4 }[/math], and discriminant [math]\displaystyle{ D }[/math]. For any integer [math]\displaystyle{ n }[/math], we give an upper bound on the number of integral solutions of [math]\displaystyle{ Q(X)=n }[/math] in terms of [math]\displaystyle{ n }[/math], [math]\displaystyle{ k }[/math], and [math]\displaystyle{ 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]\displaystyle{ \mathbb{T}^d }[/math] for [math]\displaystyle{ d\geq 5 }[/math]. This conjecture is motivated by the work of Berry\cite{Berry, Michael} on semiclassical eigenfunction hypothesis.
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