Events for 11/17/2021 from all calendars

Probability Seminar

Time: 10:00AM - 11:00AM

Location: Zoom

Speaker: Chiara Franceschini, Universidade de Lisboa

Title: Markov duality for interacting particle systems

Abstract: In this talk I will overview the concept of duality for Markov processes and, in particular, some special classes of interacting particle systems. I will explain how such relations arise naturally from an algebraic description of the models and I will give some ideas on how to characterize the stationary measure using the dual, simpler, model. This is done in a context where the initial models are connected with boundary reservoirs, creating a non-equilibrium setting.

Number Theory Seminar

Time: 11:00AM - 12:00PM

Location: BLOC 628

Speaker: Shuhui Shi, Texas A&M University

Title: Eulerian multiple zeta values in positive characteristic and their motivic Galois groups

Abstract: A multiple zeta value over Fq[t] (abbreviated as MZV) is Eulerian if it is a rational multiple of a power of the Carlitz period. By the work of Anderson and Thakur, every MZV is closely related to the periods of an explicitly constructed t-motive, whose motivic Galois group, coming from Papanikolas’ Tannakian duality theory, is a linear algebraic group over Fq(t). A conjecture of Lara and Thakur on Eulerian MZV’s implies that their corresponding motivic Galois groups are of dimension 1. Assuming Lara-Thakur’s conjecture, in this talk, we give the explicit defining equations of these 1 dimensional motivic Galois groups.

Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: William Pazner, LLNL

Title: Low-order methods for high-order finite element discretizations and solvers

Abstract: In this talk, I will discuss two applications of low-order methods to increase the efficiency and robustness of high-order finite element discretizations and solvers. In the first part of the talk, I will discuss matrix-free linear solvers for high-order discontinuous Galerkin discretizations of elliptic problems. These solvers are based on the spectral equivalence of the high-order discretization with a low-order refined discretization (often known as the "FEM-SEM equivalence"). A novel extension of this equivalence to the case of nonconforming meshes and variable polynomial degrees will be presented. Using the subspace correction (additive Schwarz) framework, robust preconditioners for DG discretizations with (nonconforming) hp-refinement will be constructed that result in uniform convergence with respect to mesh size, polynomial degree, and DG penalty parameter. This method is amenable for use on adaptively refined meshes with any degree of irregularity. Examples are shown using the interior penalty and BR2 methods. In the second part of the talk, I will discuss the construction of invariant domain preserving discontinuous Galerkin methods using subcell convex limiting (cf. Guermond and Popov, 2016). The high-order DG method is augmented with a sparse low-order Lax-Friedrichs discretization constructed on a refined mesh. A key feature is that the low-order method does not become more dissipative as the polynomial degree of the high-order method is increased, in contrast with other graph viscosity techniques. The high-order and low-order methods are blended using an efficient dimension-by-dimension convex limiting procedure that can be used to guarantee the preservation of any number of user-specified convex invariants while retaining subcell resolution. Several numerical examples for the Euler equations will be shown, for which this method preserves the positivity of density, pressure and internal energy, and satisfies a minimum principle for the specific entropy.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: online

Speaker: Rachel Skipper, Ohio State University

Title: Braiding groups of homeomorphisms of Cantor sets

Abstract: We'll discuss how to braid the Grigorchuk group and other groups acting on the boundary of the tree as well as how these groups fit in to the recent developments in big mapping class groups. The talk will include works done in collaboration with Xiaolei Wu and Matthew Zaremsky.

Topology Seminar

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Erkao Bao, University of Minnesota

Title: An invitation to contact homology

Abstract: Contact homology is an invariant of the contact structure, which is an odd-dimensional counterpart of a symplectic structure. It was proposed by Eliashberg, Givental and Hofer in 2000. The application of contact homology and its variants include distinguishing contact structures, knot invariants, the Weinstein conjecture and generalization, and calculating Gromov-Witten invariants. In this talk, I will start with the notion of contact structures, then give a heuristic definition of the contact homology as an infinite dimensional Morse homology, and explain the major difficulties to make the definition rigorous. In the very end, I will talk about the chain homotopy type of contact differential graded algebra. This is a joint work with Ko Honda.