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Postdoc Colloquium Series

Fall 2017

Date:October 11, 2017
Time:4:00pm
Location:Bloc 220
Speaker:Isaac Harris , TAMU
Title:Inverse scattering for materials with a conductive boundary
Abstract:In this talk, we will consider the inverse scattering problem for a material with a conductive boundary. We will see that the shape of the object can be uniquely determined by the scattering data. Next, we turn our attention to the associated transmission eigenvalue problem. The transmission eigenvalue problem corresponds to a differential operator that contains the material parameters and therefore hold information about the coefficients.

Date:October 25, 2017
Time:4:00pm
Location:Bloc 220
Speaker:Dean Baskin, TAMU
Title:Radiation fields for wave equations
Abstract:Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a variety of contexts, starting with the familiar one dimensional wave equation and moving to the semilinear wave equation in three dimensions, the linear wave equation on the exterior of a non-rotating black hole, and then on a class of time-dependent spacetimes. Although the object of study is the same in each case, the methods used are quite different in the time-independent and time-dependent settings.

Date:November 1, 2017
Time:4:00pm
Location:Bloc 220
Speaker:Robin Tucker-Drob, TAMU
Title:Treeability and planarity in measured group theory
Abstract:A group G is called strongly treeable if the orbit equivalence relation associated to any free probability measure preserving action of G can be measurably structured by trees. I will discuss joint work with Clinton Conley, Damien Gaboriau, and Andrew Marks in which we show that all groups with planar Cayley graphs are strongly treeable. This provides the first examples of groups with one end which are strongly treeable.

Date:November 8, 2017
Time:4:00pm
Location:Bloc 220
Speaker:Cecilia Mondaini, TAMU
Title:Analysis of a feedback-control based data assimilation algorithm
Abstract:Forecasts of the future state of a complex physical system (e.g., the atmosphere) that are purely generated from a theoretical model are commonly affected by the limitations of the model inadequately representing reality. Data assimilation is the technique that combines the theoretical model with information from physical observations in order to obtain a better prediction of the future state of the system. In this talk, I will show some analytical results concerning a certain data assimilation algorithm based on feedback control. This is based on joint works with A. Biswas, C. Foias and E. S. Titi.

Date:November 15, 2017
Time:4:00pm
Location:Bloc 220
Speaker:Julia Plavnik, Texas A&M University
Title:On the classification of modular tensor categories
Abstract:The problem of classifying modular tensor categories is motivated by applications to topological quantum computation as algebraic models for topological phases of matter. These categories have also applications in different areas of mathematics like topological quantum field theory, von Neumann algebras, representation theory, and others. In this talk, we will start by introducing some of the basic definitions and properties of fusion, braided, and modular tensor categories, and we will also give some concrete examples to have a better understanding of their structures. The idea of the talk is to give an overview of the current situation of the classification program for modular categories. We will explain some of the techniques that we found useful to push further the classification, with a focus on new constructions of modular tensor categories. If time allows, we will mention some results for the super-modular case.

Date:November 21, 2017
Time:4:00pm
Location:Bloc 220
Speaker:Pavlos Motakis, Texas A&M University
Title:A metric interpretation of reflexivity for Banach spaces
Abstract:See http://www.math.tamu.edu/~iharris/Motakis.pdf

Date:November 29, 2017
Time:4:00pm
Location:Bloc 220
Speaker:Anne Shiu, Texas A&M University
Title:Geometry and dynamics of reaction systems
Abstract:Chemical reaction networks are directed graphs in which each edge represents a chemical reaction. The most basic kinetics to assign to reaction networks are those of mass-action, first introduced 150 years ago by Guldberg and Waage: the rate at which each reaction occurs is proportional to the product of the concentrations of its reactants. The systematic study of the resulting polynomial ordinary differential equations began in the 1970s, and in recent years, this area has seen renewed interest, due in part to applications to systems biology. This talk will survey progress on long-standing questions pertaining to the dynamics of reaction systems, particularly their multistationarity and long-term stability, using methods from combinatorics and polyhedral as well as toric geometry.