Difference between revisions of "Analysis Seminar"

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(Summer/Fall 2017 Analysis Seminar Schedule)
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===Naser Talebizadeh Sardari===
  
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Quadratic forms and semiclassical eigenfunction hypothesis
 
 
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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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Revision as of 21:17, 10 August 2017

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 12 Person Institution Title Sponsor
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 Person Institution Title Sponsor
October 17 David Beltran Birmingham 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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Name

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Naser Talebizadeh Sardari

Quadratic forms and 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