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Texas A&M University
Mathematics

Events for 02/01/2017 from all calendars

Student Working Seminar in Groups and Dynamics

iCal  iCal

Time: 1:00PM - 2:00PM

Location: BLOC 624

Speaker: Justin Cantu, Texas A&M University

Title: Cellular Automata


Number Theory Seminar

iCal  iCal

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

iCal  iCal

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

iCal  iCal

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

iCal  iCal

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.