# Difference between revisions of "Analysis Seminar"

Analysis Seminar

The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.

# Summer/Fall 2017 Analysis Seminar Schedule

 date speaker title host(s) institution 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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### Name

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Abstract

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.