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Events for November 10, 2017 from General and Seminar calendars

Nonlinear Partial Differential Equations

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Luan T. Hoang, Texas Tech University

Title: Nonlinear PDEs (joint with Mathematical Physics Seminar)

Abstract:
Title: Large-time asymptotic expansions for solutions of Navier-Stokes equations

Abstract: We study the long-time behavior of solutions to the three-dimensional Navier-Stokes equations of viscous, incompressible fluids with periodic boundary conditions. The body forces decay in time either exponentially or algebraically. We establish the asymptotic expansions of Foias-Saut-type for all Leray-Hopf weak solutions. If the force has an asymptotic expansion, as time tends to infinity, in terms of exponential functions or negative-power functions, then any weak solution admits an asymptotic expansion of the same type. Moreover, when the force's expansion holds in Gevrey spaces, which have much stronger norms than the Sobolev spaces, then so does the solution's expansion. This extends the previous results of Foias and Saut in Sobolev spaces for the case of potential forces.

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Luan T. Hoang, Texas Tech University

Title: Large-time asymptotic expansions for solutions of Navier-Stokes equations (Joint with Nonlinear PDEs Seminar)

Abstract: We study the long-time behavior of solutions to the three-dimensional Navier-Stokes equations of viscous, incompressible fluids with periodic boundary conditions. The body forces decay in time either exponentially or algebraically. We establish the asymptotic expansions of Foias-Saut-type for all Leray-Hopf weak solutions. If the force has an asymptotic expansion, as time tends to infinity, in terms of exponential functions or negative-power functions, then any weak solution admits an asymptotic expansion of the same type. Moreover, when the force's expansion holds in Gevrey spaces, which have much stronger norms than the Sobolev spaces, then so does the solution's expansion. This extends the previous results of Foias and Saut in Sobolev spaces for the case of potential forces.

This talk is based on joint research projects with Dat Cao (Texas Tech University) and Vincent Martinez (Tulane University).

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 117

Speaker: Henry Tucker, UC San Diego

Title: Invariants and realizations of near-group fusion categories

Abstract: Classification of fusion categories by possible ring structures realized by the tensor product was first considered by Eilenberg-Mac Lane in the case where all objects are invertible under the tensor product, i.e. the Grothendieck ring is a group ring. More recently Tambara-Yamagami, Izumi, Evans-Gannon, and others have established classification results for near-group fusion categories: those with a Grothendieck ring with basis a monoid consisting of a group adjoined with a single non-invertible element. In this talk we will survey the classification results on these categories with an emphasis on the dichotomy between the cases determined by the integrality of the non-invertible object. Specifically, in the integral case it is known that the categories are group-theoretical, and in this case we will discuss quasi-Hopf algebra realizations given by cleft extensions.

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Florin Boca, University of Illinois at Urbana-Champaign

Title: Farey statistics and the distribution of eigenvalues in large sieve matrices

Abstract: Some parts of the fine distribution of Farey fractions (a.k.a. roots of unity) is captured by their spacing statistics (consecutive gaps and correlations). A large sieve matrix is a N x N matrix A*A, where A is a Vandermonde type matrix defined by roots of unity of order at most Q. The classical large sieve inequality provides an upper bound estimate for the largest eigenvalue of A*A. This talk will discuss some connections between these topics. We will focus on the behavior of these matrices when N ~ cQ^2, with Q --> infty and c>0 constant, establishing asymptotic formulas for their moments and proving the existence of a limiting distribution for their eigenvalues as a function of c. This is joint work with Maksym Radziwill.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Alicia Harper, Brown University

Title: Factorization of maps of Deligne-Mumford stacks

Abstract: The weak factorization theorem provides a tool for explicitly relating birational varieties by a sequence of smooth blowups and blowdowns. In the setting of Deligne-Mumford stacks, one can hope to do something similar, but first one has to grapple with the fact that stacks also carry a local group structure, and thus one needs to use root stacks, a geometric operation that only exists in the stacky world, in addition to blowups and blowdowns. In this talk I will give a - not too technical - introduction to the above concepts, then discuss how to actually go about proving a stacky weak factorization theorem for non-representable morphisms.