Events for 11/04/2022 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 09:00AM - 10:00AM

Location: Zoom

Speaker: Benjamin McKenna, Harvard

Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance

Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Christopher O'Neill , San Diego State University

Title: Numerical semigroups, minimal presentations, and posets

Abstract: A numerical semigroup is a subset S of the natural numbers that is closed under addition. One of the primary attributes of interest in commutative algebra are the relations (or trades) between the generators of S; any particular choice of minimal trades is called a minimal presentation of S (this is equivalent to choosing a minimal binomial generating set for the defining toric ideal of S). In this talk, we present a method of constructing a minimal presentation of S from a portion of its divisibility poset. Time permitting, we will explore connections to polyhedral geometry. No familiarity with numerical semigroups or toric ideals will be assumed for this talk.