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Math Calendar

Upcoming Events

January 22, 2020 (Wednesday), 3:30 pm

Graduate Student Tea

Graduate Student Tea

Location: Stevenson 1425

January 22, 2020 (Wednesday), 4:10 pm

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.

January 24, 2020 (Friday), 3:00 pm

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

January 24, 2020 (Friday), 4:10 pm

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.

January 24, 2020 (Friday), 4:10 pm

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.

January 28, 2020 (Tuesday), 10:00 am

Geometry Seminar

Talk Title TBA

Jocelyne Ishak, Vanderbilt University
Location: Stevenson 1320

January 29, 2020 (Wednesday), 4:10 pm

Topology & Group Theory Seminar

Talk Title TBA

Denis Osin, Vanderbilt University
Location: Stevenson 1308

February 4, 2020 (Tuesday), 3:00 pm

Number Theory Seminar

Talk Title TBA

John Voight, Dartmouth College
Location: Stevenson 1320

February 5, 2020 (Wednesday), 4:10 pm

Topology & Group Theory Seminar

Talk Title TBA

Michael Ben-Zvi, Tufts University
Location: Stevenson 1308

February 7, 2020 (Friday), 4:10 pm

PDE Seminar

Talk Title TBA

Geng Chen, University of Kansas
Location: Stevenson 1307

February 12, 2020 (Wednesday), 4:10 pm

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.

February 13, 2020 (Thursday), 4:10 pm

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.

February 19, 2020 (Wednesday), 4:10 pm

Topology & Group Theory Seminar

Talk Title TBA

Talia Fernós, University of North Carolina, Greensboro
Location: Stevenson 1308

February 20, 2020 (Thursday), 4:10 pm

Colloquium

Talk Title TBA

Eitan Tadmor, University of Maryland
Location: Stevenson 1206

February 21, 2020 (Friday), 4:10 pm

PDE Seminar

Talk Title TBA

Lan-Hsuan Huang, University of Connecticut
Location: Stevenson 1307

February 26, 2020 (Wednesday), 4:10 pm

Topology & Group Theory Seminar

Talk Title TBA

Carolyn Abbott, Columbia University
Location: Stevenson 1308

February 27, 2020 (Thursday), 1:00 pm

Number Theory Seminar

Talk Title TBA

Marie Jameson, University of Tennessee
Location: Stevenson 1320

 

 

 

February 28, 2020 (Friday), 4:10 pm

PDE Seminar

Talk Title TBA

Leonardo Abbrescia, Michigan State University
Location: Stevenson 1307

March 25, 2020 (Wednesday), 4:10 pm

Topology & Group Theory Seminar

Talk Title TBA

Michael Hull, University of North Carolina, Greensboro
Location: Stevenson 1308

 

 

April 9, 2020 (Thursday), 4:10 pm

Colloquium

Talk Title TBA

Juhi Jang, University of Southern California
Location: Stevenson 1206

April 10, 2020 (Friday), 4:10 pm

PDE Seminar

Talk Title TBA

Casey Rodriguez, Massachusetts Institute of Technology
Location: Stevenson 1307

May 1, 2020 (Friday), 4:10 pm

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.