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Events for November 7, 2017 from General and Seminar calendars

Working Seminar in Orbit Equivalence and Measured Group Theory

Time: 10:00AM - 11:00AM

Location: BLOC 624

Speaker: Mehrzad Monzavi

Title: Stable Actions and Relative Property (T) II

Abstract: I will continue the proof of the following theorem; if the pair (G,C) does not have property (T), then G is stable.

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Suncica Canic, University of Houston

Title: Nonlinear PDEs Seminar

Title: A mathematical framework for proving existence of weak solutions to a class of fluid-structure interaction problems

The focus of this talk will be on nonlinear moving-boundary problems involving incompressible, viscous fluids and elastic structures. The fluid and structure are coupled via two sets of coupling conditions, which are imposed on a deformed fluid-structure interface. The main difficulty in studying this class of problems from the analysis and numerical points of view comes from the strong geometric nonlinearity due to the nonlinear fluid-structure coupling. We have recently developed a robust framework for proving existence of weak solutions to this class of problems, allowing the treatment of various structures (Koiter shell, multi- layered composite structures, mesh-supported structures), and various coupling conditions (no-slip and Navier slip). The existence proofs are constructive: they are based on the time-discretization via Lie operator splitting, and on our generalization of the famous Lions-Aubin-Simon’s compactness lemma to moving boundary problems. The constructive proof strategy can be used in the design of a loosely-coupled partitioned scheme, in which the fluid and structure sub-problems are solved separately, with the cleverly designed boundary conditions to enforce the coupling in a way that approximates well the continuous energy of the coupled problem. This provides stability and uniform energy estimates, important for the convergence proof of the numerical scheme. Applications of this strategy to the simulations of real-life problems will be shown. They include the flow of blood in a multi-layered coronary artery treated with vascular devices called stents (with Dr. Paniagua (Texas Heart Institute) and Drs. Little and Barker, Methodist Hospital, Houston), and optimal design of micro- swimmers and bio-robots (with biomed. engineer Prof. Zorlutuna, Notre Dame).

Parts of the mathematical work are joint with B. Muha

Analysis/PDE Reading Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 624

Speaker: Boris Hanin, TAMU

Title: Introduction to the Quantum Hall Effect

Abstract: The Quantum Hall effect concerns the low temperature behavior of many electrons confined to a two dimensional sample, such as the surface of a semi-conductor, and subjected to a strong perpendicular magnetic field. In their seminal experiments in the early 1980’s, Von Klitzing-Dorda-Pepper and Tsui-Stormer-Gossard discovered that the so-called Hall conductance is robustly and precisely quantized. This lead to much to much work so-called topological phases of matter and topological insulators. In this talk, I will give a gentle introduction to the QHE, with a focus on the basic examples. I will then briefly describe what is known about the partition function for the simplest and most important QHE wavefunction introduced by Laughlin. I will end with an open question about partition functions for important generalizations of the Laughlin wavefunctions, called incompressible states boundaryless states. The analysis of these wavefunctions is thought to involve conformal field theory and topological recursion in more than one dimension.

Student/Postdoc Working Geometry Seminar

Time: 5:00PM - 6:00PM

Location: BLOC 628

Speaker: E. Ventura, TAMU

Title: Tensor rank is not multiplicative under the tensor product, after Christiandl et. al.