Events for 03/18/2025 from all calendars

Combinatorial Algebraic Geometry

Time: 12:50PM - 1:40PM

Location: Bloc 302

Speaker: Frank Sottile, Texas A&M University

Title: A bestiary of Bloch varieties

Abstract: (This is a reprise of the talk in the MPHA seminar on Friday, March 7.)
To a Z^d-periodic weighted graph with vertices V, we may associated a periodic graph operator that acts on ℓ₂(V). After Floquet transform, we obtain its Bloch variety, which is an algebraic hypersurface in T^d×R whose projection to R is the spectrum of the operator. Features on Bloch varieties such as Dirac (double) points, critical points, and their level sets (Fermi varieties) reflect spectral properties of the operator.
    With students Faust and Robinson, and using the Brazos cluster, we investigated over 2.1 million small periodic graphs, recording invariants and features of their Bloch and Fermi varieties. In this talk, I will briefly discuss the background and present some examples of interesting behavior of Bloch varieties that we uncovered.

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: BLOCKER 302

Speaker: Tomasz Komorowski, Polish Academy of Sciences

Title: Energy propagation in stochastically perturbed harmonic chains.

Abstract: Nature has a hierarchical structure with macroscopic behavior arising from the dynamics of atoms and molecules. The connection between different levels of the hierarchy is however not always straightforward, as seen in the emergent phenomena, such as phase transition and heat convection. Establishing in a mathematical precise way the connection between the different levels is the central problem of rigorous statistical mechanics. One of the methods leading to such results is to introduce some stochasticity inside the system. A classical microscopic model of the thermal energy transport is provided by a chain of coupled oscillators on a integer lattice, that describes atoms (or molecules) in a crystal. We summarise some of the results obtained recently concerning the derivation of the macroscopic heat equation from the microscopic behaviour of a harmonic chain with a stochastic perturbation. We focus our attention on the emergence of macroscopic boundary conditions. The results have been obtained in collaboration with Joel Lebowitz, Stefano Olla, Marielle Simon.

Working Seminar on HDP

Time: 4:30PM - 5:30PM

Location: Bloc 302

Speaker: Paul Simanjuntak, Texas A&M University