Events for 10/29/2014 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Zhizhang Xie, Texas A&M University

Title: Higher Signature on Witt Spaces

Abstract: The signature is a fundamental homotopy invariant for topological manifolds. However, for spaces with singularities, this usual notion of signature ceases to exist, since, in general, spaces with singularities fail the usual Poincaré duality. A generalized Poincaré duality theorem for spaces with singularities was proven by Goresky and MacPherson using intersection homology. The classical signature was then extended to Witt spaces by Siegel using this generalized Poincaré duality. Witt spaces are a natural class of spaces with singularities. For example, all complex algebraic varieties are Witt spaces. In this talk, I will describe a combinatorial approach to the higher signature of Witt spaces, using methods of noncommutative geometry. This is based on joint work with Nigel Higson.

Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Ignacio Tomas, University of Maryland

Title: PDE models for Ferrofluids and their Numerical Analysis

Abstract: A ferrofluid is a liquid which becomes strongly magnetized in the presence of applied magnetic fields. In this talk we will survey some models for ferrofluids: their physical origins, PDE models, and related numerics. There are two generally accepted ferrofluid models which we will call by the name of their developers: the Rosensweig and Shliomis model. We will start by developing a numerical scheme for the Rosensweig model and carefully track the requirements to devise of an energy-stable scheme. Both the Rosensweig and Shliomis models deal with one-phase flows, which is the case of many technological applications. However, many applications arise naturally in the form of a two-phase flow: one of the phases has magnetic properties and the other one does not (e.g. magnetic manipulation of microchannel flows, microvalves, magnetically guided transport, etc). We have also developed a matching-density two-phase ferrofluid model starting from the simplified framework of the Shliomis model and the Cahn-Hilliard equation. This model satisfies an energy law, and with the lessons learned from the Rosensweig model, we were able to devise an energy-stable scheme. In addition, with some simplifications of the two-phase model, it is possible to prove convergence of the scheme, and as a by product, existence of solutions of the simplified PDE system. Finally, I will illustrate the capabilities of the numerical schemes with some numerical simulations.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Yair Hartman, Weizmann Institute

Title: The Furstenberg entropy realization problem

Abstract: Stationary actions are a generalization of measure preserving actions, in the context of a random walk on a group. The Furstenberg entropy of a stationary action is an important invariant which measures its "distance from invariance". The realization problem is to determine the possible entropy values realizable for a given random walk. In this talk we will see a new characterization of Kazhdan's property (T) in terms of this problem (for non-singular actions) and will use Invariant Random Subgroups (IRSs) in order to describe a full solution of the problem for lamplighter groups. Based of several joint works with Lewis Bowen, Omer Tamuz and Ariel Yadin

First Year Graduate Student Seminar

Time: 5:30PM - 6:30PM

Location: BLOC 628

Speaker: Matt Papanikolas and Colleen Robles

Title: Department research groups: number theory; differential geometry.