Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Hao Guo, Texas A&M University

Title: A Lichnerowicz vanishing theorem for the maximal roe algebra

Abstract: Let M be a complete spin Riemannian manifold. Then the Dirac operator on M has an index taking values in the K-theory of the maximal Roe algebra. One of the basic properties one would like to have for this index is that it vanishes when the M has uniformly positive scalar curvature. But as distinct from the setting of the reduced Roe algebra, one cannot directly apply a functional calculus argument on the maximal Roe algebra to show this vanishing. In this talk we outline the steps to a proof of this fact using a uniform version of the maximal Roe algebra. This is joint work with Zhizhang Xie and Guoliang Yu.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Brian Simanek, Baylor

Title: Spectral Theory of Graph Laplacians and Orthogonal Polynomials

Abstract: Our main object of interest is the spectrum of the discrete Laplacian on the Cayley graph of the Lamplighter Group. We will show how the spectral theory of orthogonal polynomials is relevant to the determination of this spectrum and present some calculations that provide new examples of spectral phenomena. Based on joint work with R. Grigorchuk.

Numerical Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Uwe Kocher, Helmut-Schmidt-University, Hamburg

Title: Numerical simulation of coupled flow and deformation in porous media with space-time methods

Abstract: The efficient and accurate simulation of coupled flow and deformation in porous media in space and time is of fundamental importance in many engineering fields. The quasi-static and dynamic poroelastic models appear for instance in simulation studies to support the development of next-generation batteries. Such must support fast-charging and fast-draining with currents of a factor of at least 100 or more compared to nowadays cutting-edge technologies. Future generation numerical simulation tools must incorporate multiphysics phenomena in which sharp concentration and pressure gradients, high mechanical stresses, elastic wave propagation, memory-effects on the media parameters, multi-phase behavior, crack propagation as well as electro-chemical reactions occur. In this contribution high-order space-time discretisations, including mixed finite elements (MFEM) for the flow variables and interior-penalty discontinuous Galerkin finite elements (IPDG) for the displacement and velocity variables, are presented. The arising linear block systems are solved with a sophisticated monolithic solver technology with flexible multi-step fixed-stress physical preconditioning. Inside the preconditioner highly optimized system solvers for low order approximations can be used. Additionally, our solver technology allows for parallel-in-time application. The performance properties of the solver and for further applications are illustrated by numerical experiments.

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 220

Speaker: Dr. Igor Zelenko, Department of Mathematics, TAMU

Title: Euler characteristic, winding numbers, and can we comb a hedgehog?

Abstract: The goal of the talk is to give a glimpse into the remarkable topic of Mathematics, called Algebraic Topology on the example of solving of the following 'practical' problem: Can we comb a hedgehog? A hedgehog is called combed if there is no needle perpendicular to the surface of the hedgehog. To answer this question we need to define several remarkable integer numbers that do not change under quite large classes of deformations: the Euler number of a surface and the index of a stationary point of a vector field (which also related to a winding number of a curve) and then to relate this seemingly unrelated numbers. This kind of Mathematics should be definitely different from everything you have seen in high school and the first year of your university studies and I am sure you will not be bored.