Events for 02/16/2024 from all calendars

Stochastic Processes Seminar

Time: 10:00AM - 11:00AM

Location: BLOC 302

Speaker: Ruoyu Wu, Iowa State University

Title: Weakly interacting jump processes with graphon interactions

Abstract: We consider systems of weakly interacting jump processes on heterogeneous random graphs and their large population limit. The interaction is of mean field type weighted by the underlying graphon. A law of large numbers result is established as the system size increases and the underlying graphons converge. The limit is given by a graphon particle system consisting of independent but heterogeneous nonlinear Markovian processes whose probability distributions are fully coupled. An application to individual-based epidemic models is discussed. If time permits, a related queueing model, Join-the-shortest-queue(d), will also be discussed.

Geometry Seminar

Time: 4:00PM - 4:50PM

Location: BLOC 302

Speaker: Julia Lindberg, University of Texas

Title: On the typical and atypical solution to the Kuramoto equations

Abstract: The Kuramoto model is a dynamical system that models the interaction of coupled oscillators. There has been much work to effectively bound the number of equilibria to the Kuramoto model for a given network. By formulating the Kuramoto equations as a system of algebraic equations, we first relate the complex root count of the Kuramoto equations to the combinatorics of the underlying network by showing that the complex root count is generically equal to the normalized volume of the corresponding adjacency polytope of the network. We then give explicit algebraic conditions under which this bound is strict and show that there are conditions where the Kuramoto equations have infinitely many equilibria.