Events for 02/24/2017 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Jeremy Marzuola, University of North Carolina

Title: Ground states for nonlinear Schrödinger equation on a dumbbell graph

Abstract: With Dmitry Pelinovsky, we describe families of standing waves on a closed quantum graph in the shape of a dumbbell, namely having two loops connected by a link with Kirchhoff boundary conditions.  We describe symmetry breaking bifurcations and prove a remarkable asymptotic property that is a bit surprising in terms of the energy minimizing solutions at a given mass.

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Luis David Garcia-Puente, Sam Houston State University

Title: Counting arithmetical structures

Abstract: Let G be a finite, simple, connected graph. An arithmetical structure on G is a pair of positive integer vectors d,r such that (diag(d)−A)r=0, where A is the adjacency matrix of G. Arithmetical graphs were introduced in the context of arithmetical geometry by Lorenzini in 1989 to model intersections of curves. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the cokernels of the matrices (diag(d)−A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients C(2n−1, n−1), and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: JM Landsberg, TAMU

Title: Symmetry v. Optimality

Abstract: The talk will be a colloquium style talk - all are welcome. I will discuss uses of algebraic geometry and representation theory in complexity theory. I will explain how these geometric methods have been successful in proving lower complexity bounds: unblocking the problem of lower bounds for the complexity of matrix multiplication, which had been stalled for over thirty years, and providing the first exponential separation of the permanent from the determinant in any restricted model. (The permanent v. determinant problem is an algebraic cousin of the P v. NP problem.) I will also discuss exciting new work that indicates that these methods can also be used to provide complexity upper bounds, in fact construct explicit algorithms. This is joint work with numerous co-authors including G. Ballard, A. Conner, C. Ikenmeyer, M. Michalek, G. Ottaviani, and N. Ryder.