MenuEvents for 11/18/2016 from all calendars
Working Seminar on Quantum Groups
Time: 11:00AM - 12:00PM
Location: BLOC 628
Speaker: Michael Brannan, TAMU
Title: Quantum subgroups, topological generation, and applications
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:50PM
Location: BLOC 628
Speaker: Semyon Dyatlov, MIT
Title: Resonances for open quantum maps
Abstract: Quantum maps are a popular model in physics: symplectic relations on tori are quantized to produce families of $N\times N$ matrices and the high energy limit corresponds to the large $N$ limit. They share a lot of features with more complicated quantum systems but are easier to study numerically. We consider open quantum baker's maps, whose underlying classical systems have a hole allowing energy escape. The eigenvalues of the resulting matrices lie inside the unit disk and are a model for scattering resonances of more general chaotic quantum systems. However in the setting of quantum maps we obtain results which are far beyond what is known in scattering theory. We establish a spectral gap (that is, the spectral radius of the matrix is separated from 1 as $N\to\infty$) for all the systems considered. The proof relies on the notion of fractal uncertainty principle and uses the fine structure of the trapped sets, which in our case are given by Cantor sets, together with simple tools from harmonic analysis, algebra, combinatorics, and number theory. We also obtain a fractal Weyl upper bound for the number of eigenvalues in annuli. These results are illustrated by numerical experiments which also suggest some conjectures. This talk is based on joint work with Long Jin.
Linear Analysis Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 220
Speaker: Sujan Pant, University of Iowa
Title: Structural results for von Neumann algebras arising from poly-hyperbolic groups and Burger-Mozes groups
URL: Event link
Student Working Seminar in Groups and Dynamics
Time: 3:00PM - 4:00PM
Location: BLOC 624
Speaker: Mehrzad Monzavi, TAMU
Title: Geodesic Tracking Lemma
Abstract: When a trajectory goes almost along a geodesic ray, the random walk on the geodesic metric space is said to have the geodesic tracking property. In this talk, we will prove a lemma by Kaimanovich in the case of a random walk on groups acting on a hyperbolic space under finite first moment condition.
Algebra and Combinatorics Seminar
Time: 3:00PM - 3:50PM
Location: BLOC 628
Speaker: Nathan Mehlhop, Texas A&M University
Title: Cyclic Resultants and Approximation of Amoebas
Abstract: The amoeba of a Laurent polynomial is the projection of its corresponding hypersurface under a Log absolute value map. Amoebas have applications in various mathematical subjects. The computation and approximation of amoebas is known to be a challenging problem which has been tackled by several authors in recent years. In this presentation, I show an approximation method that was described theoretically by Purbhoo and show that its runtime can be drastically reduced by exploiting properties of iterated cyclic resultants which will be derived.
Douglas Lectures
Time: 4:00PM - 5:00PM
Location: BLOCKER 117
Speaker: Hari Bercovici, Indiana University
Title: Eigenvalues of sums of matrices: Singular values and invariant factors
Abstract: There are questions about singular values and invariant factors for products of matrices (scalar or over more complicated rings) that can be answered using the elementary intersection theory discussed in the second lecture. We show how one can use intersection theory to produce invariant subspaces with specified properties, for instance, for linear operators on a finite dimensional space.
Geometry Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 628
Speaker: Tim Magee, UT Austin
Title: Log Calabi-Yau mirror symmetry and representation theory
Abstract: Mark Gross, Paul Hacking, Sean Keel, and Bernd Siebert have been developing a mirror symmetry program for log CYs-- varieties U that come with a unique volume form Ω having at worst a simple pole along any divisor in any compactification of U. My goal will be to convince you that this mirror symmetry program actually gives a nice back door into representation theory. I'll focus on a particular example-- finding the structure constants for decomposing a tensor product of GL_n irreps into a sum, the “Littlewood- Richardson coefficients”. We'll get the Knutson-Tao hive cone encoding these constants as part of a broader framework, one that in principal has nothing to do with representation theory at all and should only depend upon having a variety with the right type of volume form.
