Location: Stevenson 1425

Denis Osin, Vanderbilt University
Location: Stevenson 1308

I will explain how to use basic tools of descriptive set theory to show that a closed set S of marked groups has 2ℵ0 quasi-isometry classes provided every non-empty open subset of S contains at least two non-quasi-isometric groups. It follows that every perfect set of marked groups having a dense subset of finitely presented groups contains 2ℵ0 quasi-isometry classes. These results account for most known constructions of continuous families of non-quasi-isometric finitely generated groups. They can also be used to prove the existence of 2ℵ0 quasi-isometry classes of finitely generated groups having interesting algebraic, geometric, or model-theoretic properties. This talk is based on a joint work with A. Minasyan and S. Witzel.

John Voight, Dartmouth College
Location: Stevenson 1320

We recognize certain special hypergeometric motives, related to and inspired by the discoveries of Ramanujan more than a century ago, as arising from Asai L-functions of Hilbert modular forms.

Spencer Dowdall, Vanderbilt University
Location: Stevenson 1206

Michael Ben-Zvi, Tufts University
Location: Stevenson 1308

Jeffrey C. Lagarias, University of Michigan
Location: Stevenson 1206

Hilbert’s 12-th Problem concerns the construction of class elds using special values of analytic functions, especially modular forms. The Stark Conjectures (work of my advisor Harold M. Stark) conjecturally construct various class elds, particularly real quadratic elds, using special values of L-functions at s = 0. We review Hilbert’s 12th problem and the Stark conjectures and describe an unexpected connection of the Stark Conjectures to the (conjectured) existence of maximal systems of complex equiangular lines in Cn, known as SIC- POVM’s in quantum information theory. The latter is work of my student Gene Kopp (PhD 2017).

Geng Chen, University of Kansas
Location: Stevenson 1307

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.

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.

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

Eitan Tadmor, University of Maryland
Location: Stevenson 1206

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

Carolyn Abbott, Columbia University
Location: Stevenson 1308

Marie Jameson, University of Tennessee
Location: Stevenson 1320

Leonardo Abbrescia, Michigan State University
Location: Stevenson 1307

Marek Kaluba, Adam Mickiewicz University, Poland
Location: Stevenson 1308

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

Juhi Jang, University of Southern California
Location: Stevenson 1206

Casey Rodriguez, Massachusetts Institute of Technology
Location: Stevenson 1307

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.