Events for 10/19/2022 from all calendars

Postdoc Talks/Lunch

Time: 11:30AM - 12:45PM

Location: BLOC 302

Description: 11:30a.m.
Dr. Matthias Hofmann
Title: Clustering problems on quantum graphs

Abstract: We introduce quantum graphs and motivate their relevance in the context of networks. We compare known results for eigenvalue problems to counterparts for metric graphs. These eigenvalue problems can be related to competing species problems and can be described via spectral minimal partition problems, recently introduced in Kennedy et al [CVPDE 60 (2021), 61]. We present existence results for spectral minimal partitions and show sharp lower and upper estimates for various spectral minimal energies, estimates between these energies and eigenvalues of the Laplacian and discuss their asymptotic behaviour. Other ways to identify clusters in networks can be obtained by identifying nodal domains of eigenfunctions of appropriate operators. In this context we present Pleijel and Weyl-type theorems on the asymptotics of the number of nodal domains ν_n of the n-th eigenfunction(s) of a broad class of operators of Schrödinger type. Among other things, these results characterize the accumulation points of the sequence {ν_n/n}_(n∈N), which are shown always to form a finite subset of (0,1].

Abstract: This talk discusses generalized Nash equilibrium problems that are given by rational functions. Rational expressions for Lagrange multipliers and feasible extensions of KKT points are introduced to compute generalized Nash equilibria (GNEs). We give a hierarchy of rational optimization problems to solve rational generalized Nash equilibrium problems. The Moment-SOS relaxations are applied to solve the rational optimization problems.

Abstract: Entropy is an important numerical isomorphism invariant of pmp dynamical systems. Orbit equivalence is a relation between pmp dyna

Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Lise-Marie Imbert-Gerard, University of Arizona

Title: Wave propagation in inhomogeneous media: An introduction to quasi-Trefftz methods

Abstract: Trefftz methods rely, in broad terms, on the idea of approximating solutions to Partial Differential Equation (PDEs) using basis functions which are exact solutions of the PDE, making explicit use of information about the ambient medium. But wave propagation in inhomogeneous media is modeled by PDEs with variable coefficients, and in general no exact solutions are available.

Quasi-Trefftz methods have been introduced, in the case of the Helmholtz equation with variable coefficients, to address this problem: they rely not on exact solutions to the PDE but instead of high order approximate solutions constructed locally. We will discuss the origin, the construction, and the properties of these so-called quasi-Trefftz functions. We will also discuss the consistency error introduced by this construction process.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 506a

Speaker: Volodymyr Nekrashevych, Texas A&M University

Title: Dimensions of self-similar groups (part 2)

Abstract: Every contracting self-similar group defines the associated limit space with a natural class of metrics on it. If the group is the iterated monodromy group of a locally expanding covering map of a compact metric space X, then the limit space is canonically homeomorphic to X. For example, the Julia set of a sub-hyperbolic rational function is the limit space of its iterated monodromy group (where the usual metric on the Riemann sphere belongs to the above mentioned natural class of metrics on the limit space). We will discuss how the topological dimension of the limit space can be interpreted in terms of the action of the group on the rooted tree. We will also discuss possible applications of the Ahlfors-regular dimension of the limit space (for the natural class of metrics).

Tenure Track Hiring Meeting

Time: 4:00PM - 5:00PM

Location: Bloc 117