Events for 02/01/2017 from all calendars
Student Working Seminar in Groups and Dynamics
Time: 1:00PM - 2:00PM
Location: BLOC 624
Speaker: Justin Cantu, Texas A&M University
Title: Cellular Automata
Number Theory Seminar
Time: 1:45PM - 2:45PM
Location: BLOC 220
Speaker: Andrew Bridy, Texas A&M University
Title: Dynamically distinguishing polynomials
Abstract: For p prime, consider the directed graphs induced by the polynomials x^2,x^2+1,...,x^2+p-1, viewed as mappings F_p -> F_p. Experiments suggest that these graphs are pairwise non-isomorphic for all p not in {2,17}. It is unclear how to show that this holds for all large primes. Turning the question around, we aim to construct large sets of polynomials of the form {x^k+c_1,...,x^k+c_m} so that their reductions mod p induce m pairwise non-isomorphic directed graphs for almost all primes p. We show that m can be arbitrarily large for every degree k, and in fact most m-tuples of integers (c_1,...,c_m) work. The proof uses the Galois theory of periodic points largely developed by Morton. This is joint work with Derek Garton.
URL: Event link
Noncommutative Geometry Seminar
Time: 2:00PM - 2:50PM
Location: BLOC 628
Speaker: Alexander Engel, Texas A&M University
Title: Strong Novikov conjecture and combinatorics of groups
Abstract: We will introduce higher-order Dehn functions of groups, and we will outline the main idea how polynomial bounds on these functions imply the strong Novikov conjecture. We will also discuss why, e.g., automatic groups belong to this class of groups.
Groups and Dynamics Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 220
Speaker: Volodymyr Nekrashevych
Title: On Rubin's theorem
Abstract: Rubin's theorems give conditions under which a group acting by homeomorphisms on a topological space uniquely determines (as an abstract group) the space X up to a homeomorphism. For example, a corollary of it is the fact that two manifolds are homeomorphic if and only if their homeomorphism groups are isomorphic as abstract groups. I will describe a simple group-theoretic "translation" of the proof of a Rubin's theorem, and discuss its applications.
Colloquium - Jessica Lin
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Jessica Lin
Description:
Title: Quantitative Stochastic Homogenization for Elliptic Equations
Abstract:
Stochastic homogenization is concerned with identifying the asymptotic behavior of solutions to PDEs with random coefficients. Specifically, we are interested in the following: if the coefficients are randomly varying on a microscopic lengthscale, then on average, do the random solutions exhibit the same deterministic behavior? When this is indeed the case, we say that the random equation "homogenizes." Furthermore, from both the theoretical and applied perspective, an important issue is to understand the quantitative aspects of this homogenization process. In this talk, I will present an overview of the subject of stochastic homogenization for nondivergence form elliptic equations. I will discuss the interplay between PDE and probabilistic techniques used to study these types of problems. In addition, I will present a recent quantitative result which yields the optimal error estimates on the size of the fluctuations of the random solutions. This talk is based on joint work with Scott Armstrong.