Events for 03/25/2025 from all calendars

Combinatorial Algebraic Geometry

Time: 12:50PM - 1:40PM

Location: Bloc 302

Speaker: Tianyi Yu, Université du Québec à Montréal

Title: TBA

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Blocker 302

Speaker: Marita Thomas, Freie Universitaet - Berlin

Title: First-order formulation for dynamic phase-field fracture in viscoelastic materials

Abstract: We investigate a model for dynamic fracture in viscoelastic materials. The sharp crack interface is regularized with a phase-field approximation, and for the phase-field variable a viscous evolution with a quadratic dissipation potential is employed. A non-smooth penalization prevents material healing.The viscoelastic momentum balance is formulated as a first order system and coupled in a nonlinear way to the non-smooth evolution equation of the phase field. We give a full discretization in time and space, using a discontinuous Galerkin method for the first order system. Based on this, we show the existence of discrete solutions and, as the step size in space and time tends to zero, we prove their convergence to a suitable notion of weak solution of the system. We discuss our modeling approach both at small and at finite strains and point out mathematical challenges. **This is joint work with Sven Tornquist (FUB), Christian Wieners (Karlsruhe), and Kerstin Weinberg (Siegen).

Noncommutative Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 605AX

Speaker: Gennadi Kasparov, Vanderbilt University

Title: Index theory on manifolds with a tangent Lie srtructure

Abstract: In recent years there was a significant progress in the theory of pseudo-differential operators on filtered manifolds. In my talk I will introduce a wider class of manifolds which I call manifolds with a tangent Lie structure. I will explain a coarse approach to pseudo-differential theory which gives a simplified pseudo-differential calculus containing only operators of order 0 and negative order. This calculus easily leads to the Atiyah-Singer type index theorem for operators of order 0 on manifolds with a tangent Lie structure. For filtered manifolds this calculus agrees with the known Hormander and van Erp - Yuncken calculi, which allows to extend the index theorem to operators of any order.