Fall 2021 and Spring 2022 Analysis Seminars: Difference between revisions
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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>k</math> variables, where <math>k\geq4</math>, and discriminant | Let <math>Q(X)</math> be any integral primitive positive definite quadratic form in <math>k</math> variables, where <math>k\geq4</math>, and discriminant <math>D</math>. For any integer <math>n</math>, we give an upper bound on the number of integral solutions of <math>Q(X)=n</math> in terms of <math>n</math>, <math>k</math>, and <math>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>\mathbb{T}^d</math> for <math>d\geq 5</math>. This conjecture is motivated by the work of Berry\cite{Berry, Michael} on semiclassical eigenfunction hypothesis. | ||
===Name=== | ===Name=== | ||
Revision as of 18:05, 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
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 [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.
Name
Title
Abstract