Events for 11/12/2024 from all calendars

Nonlinear Partial Differential Equations

Time: 10:00AM - 11:00AM

Location: Online

Speaker: Helmut Abels, University Regensburg

Title: Sharp Interface Limit of a Navier-Stokes/Allen-Cahn System

Abstract: We consider the sharp interface limit of a Navier-Stokes/Allen-Cahn system, when a parameter $\varepsilon>0$ that is proportional to the thickness of the diffuse interface tends to zero, in a two dimensional bounded domain. In dependence on the mobility coefficient in the Allen-Cahn equation in dependence on $\varepsilon>0$ different limit systems or non-convergence can occur. In the case that the mobility vanishes as $\varepsilon$ tends to zero slower than quadratic or does not vanish we prove convergence of solutions to a smooth solution of a corresponding sharp interface model for well-prepared and sufficiently smooth initial data. In the first case the proof is based on a relative entropy method and the construction of sufficiently smooth solutions of a suitable perturbed sharp interface limit system. In the second case it is based on the construction of a suitable approximate solution and estimates for the linearized operator. This is a joint work with Julian Fischer and Maximilian Moser (ISTA Klosterneuburg, Austria) and Maximilian Moser and Mingwen Fei (Anhui Normal University, Wuhu, China), respectively.

Student/Postdoc Working Geometry Seminar

Time: 1:00PM - 2:00PM

Location: BLOC 302

Speaker: Derek Wu, Texas A&M

Title: Generic Initial Ideals IX: Macaulay-Gotzmann Estimates on the Growth of Ideals (note special day and time)

Topology Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 605AX

Speaker: Francis Bonahon, Michigan State University

Title: Invisible SL_n-skeins

Abstract: For a Lie group G, the G-skein module of a 3-dimensional manifold M is a fundamental object in Witten’s interpretation of quantum knot invariants in the framework of a topological quantum field theory. It depends on a parameter q and, when this parameter q is a root of unity, the G-skein module contains elements with a surprising “invisibility” property, in the sense that they can be traversed by any other skein without changing the resulting total skein. I will describe some of these invisible elements in the case of the special linear group SL_n. The construction is based on the very classical theory of symmetric polynomials in n variables.