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# Departmental Colloquia

Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in Parker Hall, Room 250 (unless otherwise advertised) with refreshments preceding at 3:30pm in Parker Hall, Room 244.

DMS Colloquium: Lori Alvin

Nov 09, 2018 04:00 PM

Speaker: Lori Alvin

Faculty host: Krystyna Kuperberg

DMS Colloquium: Kevin K Lin

Oct 19, 2018 04:00 PM

Speaker: Kevin K Lin, College of Mathematical Sciences, University of Arizona

Title: Mori--Zwanzig formalism and discrete-time modeling of chaotic dynamics

Abstract: Nonlinear dynamic phenomena often require a large number of dynamical variables to model, only a small fraction of which are of direct interest.  Reduced models that use only the relevant dynamical variables can be very useful in such situations, both for computational efficiency and insights into the dynamics.  Recent work has shown that the NARMAX (Nonlinear Auto-Regressive Moving-Average with eXogenous inputs) representation of stochastic processes provides an effective basis for parametric model reduction in a number of concrete settings [Chorin-Lu PNAS 2015].  In this talk, I will review these developments as well as a general theoretical framework for model reduction due to Mori and Zwanzig.  I will then explain how the NARMAX method can be seen as a special case of the Mori-Zwanzig formalism and discuss some general implications and technical issues that arise.  These ideas will be illustrated on a prototypical model of spatiotemporal chaos.

Faculty host: Xiaoying Han

DMS Colloquium: Hal Schenk

Oct 08, 2018 04:00 PM

Speaker: Hal Schenk

Title: Wachspress varieties: algebraic geometry meets numerical analysis.

Abstract: In 1975, Wachspress introduced barycentric coordinates for a polygon as a tool for approximation theory and numerical analysis. In a recent SIAM J. Numerical Analysis paper, Floater posed the question of determining the algebraic relations among the Wachspress coordinates; this makes the process of ascertaining if a point is in the image of the Wachspress map much faster. Using tools from computational algebra and algebraic topology we provide an answer to this question (joint work with C. Irving).

DMS Colloquium: Fioralba Cakoni

Oct 05, 2018 04:00 PM

Speaker: Fioralba Cakoni (Rutgers University)

Title: Spectral Problems in Inverse Scattering for Inhomogeneous Media

Abstract: The inverse scattering problem for inhomogeneous media amounts to inverting a locally compact nonlinear mapping, thus presenting difficulties in arriving at a solution. A possible approach to this problem is to exploit spectral properties of operators associated with scattering phenomena which carry essential information about the media. The identified eigenvalues must satisfy two important properties: 1) can be determined from the scattering data, and 2) are related to geometrical and physical properties of the media in an understandable way.

In this talk we will discuss some old and new eigenvalue problems arising in scattering theory for inhomogeneous media. We will present a two-fold analysis: on one hand, relating the eigenvalues to the measurement operator (to address the first property) and, on the other hand, viewing them as the spectrum of appropriate (possibly non-self-adjoint) partial differential operators (to address the second property). Numerical examples will be presented to show what kind of information these eigenvalues yield on the unknown inhomogeneity. We end with a brief discussion on transmission eigenvalues arising in a scattering problem in the hyperbolic geometry for automorphic forms, and show that, in particular cases, they are related to the zeros of Riemann zeta function.

Faculty host: Junshan Lin

DMS Colloquium: Qingtang Su

Sep 28, 2018 04:00 PM

Speaker: Qingtang Su (University of Michigan, Ann Arbor)

Title: Long Time Behavior of the 2D Water Waves with Point Vortices

Faculty host: Yongsheng Han

DMS Colloquium: Ken Ono

Sep 27, 2018 04:00 PM

Speaker: Ken Ono, Asa Griggs Candler Professor of Mathematics (Emory University)

Title: Polya’s Program for the Riemann Hypothesis and Related Problems

Abstract: In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity has only been proved for degrees $$d=1, 2, 3$$. We prove the hyperbolicity of all (but possibly finitely many) the Jensen polynomials of every degree $$d$$. We obtain a general theorem which models such polynomials by Hermite polynomials, which in the case of the zeta-function can be thought of as a "degree aspect" GUE distribution. The general theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function.

This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.

Faculty host: Narendra Govil

DMS Colloquium: Robert Gardner

Aug 07, 2018 04:00 PM

Speaker: Robert Gardner, East Tennessee State University

Title: The Quaternions: An Algebraic and Analytic Exploration