# Math Calendar

### Upcoming Events

## Graduate Student Tea

## Graduate Student Tea

Location: Stevenson 1425

## Topology & Group Theory Seminar

## Groups Finitely Presented in Burnside Varieties

Alexander Olshanskiy, Vanderbilt University

Location: Stevenson 1308

S.V. Ivanov’s problem of 1992 has been solved. For all sufficiently large odd integers n, the following version of Higman’s embedding theorem is proved in the variety Bn of all groups satisfying the identity xn=1. A finitely generated group G from Bn has a presentation G=⟨A∣R⟩ with a finite set of generators A and a recursively enumerable set R of defining relations if and only if it is a subgroup of a group H finitely presented in the variety Bn. It follows that there is a ‘universal’ 2-generated finitely presented in Bn group containing isomorphic copies of all finitely presented in Bn groups as subgroups.

## QSBC-Mathematics Seminar

## A Systems Mechanism for KRAS Mutant Allele Specific Responses to Targeted Therapy

Ed Stites, Salk Institute for Biological Studies, La Jolla, CA

Location: Stevenson 5211

## PDE Seminar

## Self-Similarity and Naked Singularities for the Einstein Vacuum Equations

Yakov Shlapentokh-Rothman, Princeton University

Location: Stevenson 1307

We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations. Then we will discuss our previous work on the asymptotically self-similar regime for the Einstein equations and the corresponding connection to the “ambient metric” of Fefferman and Graham. Finally, we will explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to the exterior region of a naked singularity. This is all joint work with Igor Rodnianski.

## Number Theory Seminar

## Moments of Half Integral Weight Modular L-functions, Bilinear Forms and Applications

Alex Dunn, University of Illinois at Urbana-Champaign

Location: Stevenson 1310

Given a half-integral weight holomorphic newform f, we prove an asymptotic formula for the second moment of the twisted L-function over all primitive characters modulo a prime. In particular, we obtain a power saving error term and our result is unconditional; it does not rely on the Ramanujan—Petersson conjecture for the form f. This gives a very sharp Lindelöf on average result for L-series attached to Hecke eigenforms without an Euler product. The Lindelöf hypothesis for such series was originally conjectured by Hoffstein. In the course of the proof, one must treat a bilinear form in Salié sums. It turns out that such a bilinear form also has several arithmetic applications to equidistribution. These are a series of joint works with Zaharescu and Shparlinski—Zaharescu.

## Geometry Seminar

## Talk Title TBA

Jocelyne Ishak, Vanderbilt University

Location: Stevenson 1320

## Topology & Group Theory Seminar

## Talk Title TBA

Denis Osin, Vanderbilt University

Location: Stevenson 1308

## Number Theory Seminar

## Talk Title TBA

John Voight, Dartmouth College

Location: Stevenson 1320

## Topology & Group Theory Seminar

## Talk Title TBA

Michael Ben-Zvi, Tufts University

Location: Stevenson 1308

## PDE Seminar

## Talk Title TBA

Geng Chen, University of Kansas

Location: Stevenson 1307

## Topology & Group Theory Seminar

## Cusp Transitivity in Hyperbolic 3-manifolds (Joint work with Steven Tschantz)

John Ratcliffe, Vanderbilt University

Location: Stevenson 1308

Let S be a set and k an integer such that 1≤k≤|S|. An action of a group G on S is called k-transitive if for every choice of distinct elements x1,…,xk of S and every choice of distinct targets y1,…,yk in S, there is an element g of G such that gxi=yi for each i=1,…,k. The term {\it transitive} means 1-transitive, and actions with k>1 are called multiply transitive. This talk is concerned with cusped hyperbolic 3-manifolds of finite volume whose group of isometries induces a multiply transitive action on the set of cusps of the manifold. Roger Vogeler conjectured that there is a largest k for which such k-transitive actions exist, and that for each k≥3, there is an upper bound on the possible number of cusps. Our proof of Vogeler’s conjecture will be discussed in this talk.

## Colloquium

## Orthogonality Relations for GL(n)

Dorian Goldfeld, Columbia University

Location: Stevenson 1206

Orthogonality is a fundamental theme in representation theory and Fourier analysis. In the case of a finite abelian group G, the orthogonality relation for characters of G was used by Dirichlet in 1837 to prove that there are infinitely many primes in an arithmetic progressions a,a+d,a+2d,a+3d,… provided a,d are co-prime positive integers. This type of orthogonality relation occurs on GL(1) over the adele group of ℚ. When considering automorphic representations for GL(n) with n>1, however, the automorphic representations are infinite dimensional and it is not so clear how to even formulate an orthogonality relation. We shall survey what is known (including applications to number theory) and introduce new results for the real group GL(4,ℝ). This talk is based on recent joint work with Eric Stade and Michael Woodbury and is aimed at a general audience.

## Topology & Group Theory Seminar

## Talk Title TBA

Talia Fernós, University of North Carolina, Greensboro

Location: Stevenson 1308

## Colloquium

## Talk Title TBA

Eitan Tadmor, University of Maryland

Location: Stevenson 1206

## PDE Seminar

## Talk Title TBA

Lan-Hsuan Huang, University of Connecticut

Location: Stevenson 1307

## Topology & Group Theory Seminar

## Talk Title TBA

Carolyn Abbott, Columbia University

Location: Stevenson 1308

## Number Theory Seminar

## Talk Title TBA

Marie Jameson, University of Tennessee

Location: Stevenson 1320

## PDE Seminar

## Talk Title TBA

Leonardo Abbrescia, Michigan State University

Location: Stevenson 1307

## Topology & Group Theory Seminar

## Talk Title TBA

Michael Hull, University of North Carolina, Greensboro

Location: Stevenson 1308

## Colloquium

## Talk Title TBA

Juhi Jang, University of Southern California

Location: Stevenson 1206

## PDE Seminar

## Talk Title TBA

Casey Rodriguez, Massachusetts Institute of Technology

Location: Stevenson 1307

## PDE Seminar

## Generalized Localization for Spherical Partial Sums of Fourier Series

Ravshan Ashurov, Institute of Mathematics, National University of Uzbekistan

Location: Stevenson 1307

Historically progress with solving the Luzin conjecture has been made by considering easier problems. For multiple Fourier series one of such easier problems is to investigate convergence almost everywhere of the spherical sums on TN\ supp(f) (so called the generalized localization principle). For the spherical partial integrals of multiple Fourier integrals the generalized localization principle in classes Lp(RN) was investigated by many authors. In particular, in the remarkable paper of A. Carbery and F. Soria the validity of the generalized localization was proved in Lp(RN) when 2 <= p < 2N/(N – 1). In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in L2 – class is proved. It was previously known that the generalized localization was not valid in classes Lp(TN) when 1 <= p = 1: if p >= 2 then we have the generalized localization and if p < 2, then the generalized localization fails.