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

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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Extras

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