Difference between revisions of "Analysis Seminar"
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Quadratic forms and the semiclassical eigenfunction hypothesis | Quadratic forms and the semiclassical eigenfunction hypothesis | ||
| − | Let <math>Q(X)</math> be any integral primitive positive definite quadratic form in <math> | + | Let <math>Q(X)</math> be any integral primitive positive definite quadratic form in <math>k</math> 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=== | ===Name=== | ||
Revision as of 13:03, 8 September 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
Contents
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 | Title | 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
Name
Title
Abstract
Name
Title
Abstract
Name
Title
Abstract
Naser Talebizadeh Sardari
Quadratic forms and the semiclassical eigenfunction hypothesis
Let 
be any integral primitive positive definite quadratic form in 
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
