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	Brian Street	UW Madison	Title	Betsy
September 19	Michael Greenblatt	University of Illinois Chicago	Title	Stovall
September 26	Hiroyoshi Mitake	Hiroshima University	Title	Hung
October 3	Naser Talebizadeh Sardari	UW Madison	Title	Betsy
October 10	Joris Roos	UW Madison	Title	Betsy
October 17	David Beltran	Bilbao	Title	Andreas
October 24	Xiaochun Li	UIUC	Title	Betsy
November 7	Person	Institution	Title	Sponsor
November 14	Person	Institution	Title	Sponsor
November 28	Xianghong Chen	UW Milwaukee	Title	Stovall
December 5	Person	Institution	Title	Sponsor

Abstracts

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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.

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Blank Analysis Seminar Template