Events for 12/08/2021 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 10:00AM - 11:00AM

Location: BLOC 628

Speaker: Jacob Shapiro, Princeton

Title: Delocalization in the integer-valued Gaussian Field and the BKT phase of the 2D Villain model

Abstract: It is shown that the Villain model of two-component spins over two dimensional lattices exhibits slow, non-summable, decay of correlations at any temperature at which the dual integer-valued Gaussian field exhibits delocalization. For the latter, we extend the recent proof by Lammers of a delocalization transition in two dimensional graphs of degree three, to all doubly periodic graphs, in particular to Z^2. Taken together these two statements yield a new perspective on the BKT phase transition in the Villain model, and a new proof on delocalization in two dimensional integer-valued height functions. Joint with Aizenman, Harel and Peled.

Number Theory Seminar

Time: 11:00AM - 12:00PM

Location: Zoom

Speaker: Neelam Saikia, University of Virginia

Title: Frobenius trace distributions for Gaussian hypergeometric functions

Abstract: In the 1980’s, Greene defined hypergeometric functions over finite fields using Jacobi sums. The framework of his theory establishes that these functions possess many properties that are analogous to those of the classical hypergeometric series studied by Gauss, Kummer and others. These functions have played important roles in the study of Apéry-style supercongruences, the Eichler-Selberg trace formula, Galois representations, and zeta-functions of arithmetic varieties. In this talk we discuss the distributions (over large finite fields) of natural families of these functions. For the ${}_{2}F_1$ functions, the limiting distribution is semicircular, whereas the distribution for the ${}_{3}F_2$ functions is Batman distribution.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: online

Speaker: Mark Pengitore, University of Virginia

Title: Coarse embeddings and homological filling functions

Abstract: This work is joint with Rob Kropholler. In this talk, we will relate homological filling functions with coarse embeddings. In particular, we will demonstrate that a coarse embedding of a group into a group of geometric dimension 2 induces an inequality on homological Dehn functions in dimension 2. As an application of this, we are able to show that if a finitely presented group coarsely embeds into a hyperbolic group of geometric dimension 2, then it is hyperbolic. Another application is a characterization of subgroups of groups with quadratic Dehn function. If there is enough time, we will talk about various higher dimensional generalizations of our main result.

Topology Seminar

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: William Balderrama, University of Virginia

Title: Deformations of homotopy theories and spectral sequences

Abstract: A standard technique in homotopy theory is to compute something homotopical by relating it to something algebraic. A standard example is the Künneth theorem, relating the homology H_*(X x Y) to the Tor groups Tor(H_*X, H_*Y). This reflects a more general homotopical construction, namely the Künneth spectral sequence for computing tensor products of modules over ring spectra. I will describe a novel method of producing ``algebra-to-homotopy'' spectral sequences such as the latter, which proceeds by considering certain deformations of homotopy theories, both stably and unstably.