Events for 10/12/2022 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Zhaoting Wei, Texas A&M University-Commerce

Title: Grothendieck-Riemann-Roch theorem and index theorem

Abstract: It is well-known that the Hirzebruch–Riemann–Roch theorem in algebraic geometry is a special case of the Atiyah-Singer index theorem. In this talk I will present a proof of the Grothendieck-Riemann-Roch theorem as a special case of the family version of the Atiyah-Singer index theorem. In more details, we first give a Chern-Weil construction of characteristics forms of coherent sheaves in terms of antiholomorphic flat superconnections, and then give a heat-kernel proof of Grothendieck-Riemann-Roch theorem. This is a joint work with J.M. Bismut and S. Shen. ZOOM link: https://tamu.zoom.us/j/98547610481

URL: Event link

Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: David Nicholls, University of Illinois Chicago

Title: A Stable High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method for the Numerical Solution of Grating Scattering Problems

Abstract: The rapid and robust simulation of linear waves interacting with layered periodic media is a crucial capability in many areas of scientific and engineering interest. High-Order Perturbation of Surfaces (HOPS) algorithms are interfacial methods which recursively estimate scattering quantities via perturbation in the interface shape heights/slopes. For a single incidence wavelength such methods are the most efficient available in the parameterized setting we consider here.

In this talk we describe a generalization of one of these HOPS schemes by incorporating a further expansion in the wavelength about a base configuration which constitutes an "Asymptotic Waveform Evaluation" (AWE). We not only provide a detailed specification of the algorithm, but also verify the scheme and point out its benefits and shortcomings. With numerical experiments we show the remarkable efficiency, fidelity, and high-order accuracy one can achieve with an implementation of this algorithm.

Colloquium

Time: 4:00PM - 5:00PM

Location: Bloc 117

Speaker: Chris Bishop, Stony Brook University

Description: Title: Conformal Mapping in Linear Time
Abstract:  What do hyperbolic 3-manifolds have to do with the Riemann mapping theorem?  In this talk, I will explain how a theorem of Dennis Sullivan (based on an observation of Bill Thurston) about  convex sets in hyperbolic 3-space leads to a fast algorithm for computing conformal maps. The conformal map from the unit disk to the interior of a polygon is given by the Schwarz-Christoffel formula, but this formula is stated in terms of parameters that are hard to compute.  I will explain a fast way to approximate these parameters: the speed comes from the medial axis,  a type of Voronoi diagram from computational geometry, and the accuracy is proven using Sullivan's theorem.  At the end of the lecture, I will mention various  applications to discrete geometry and optimal meshing; one of these  will be the subject of the second lecture.