Events for 04/24/2018 from all calendars

Andrew Swift Thesis Defense: On some problems in nonlinear Banach space geometry

Time: 11:00AM - 12:00PM

Location: BLOC 220

Speaker: Andrew Swift

Description: Two general problems in the nonlinear geometry of Banach spaces are to determine the relationship between uniform and coarse embeddability and to characterize local/asymptotic properties in terms of metric structure. The purpose of this research is to investigate these problems and to contribute to a better overall understanding of the structure of Banach spaces and metric spaces. We use general techniques found in the literature to study three specific examples. First, we investigate the relationship between the small-scale and large-scale structures of $c_0(\kappa)$. Next, we investigate the relationship between the small-scale and large-scale structures of superstable Banach spaces. Finally, we define a vertex-labeling for a class of graphs we call the ``bundle graphs'', and use this to generalize some known characterizations of Banach space properties in terms of graph preclusion.

Maxson Lecture Series

Time: 4:00PM - 5:00PM

Location: Blocker 117

Speaker: Fernando Rodriguez-Villegas, The Abdus Salam International Centre for Theoretical Physics

Title: Maxson Lecture II: Combinatorics and geometry

Abstract: Thanks to the work of A. Weil we know that counting points of varieties over finite fields yields purely topological information about them. For example, the complex points of an algebraic curve consist of a certain number g, its genus, of donuts glued together. On the other hand the genus determines how the number of points of the curve has over a finite field grows as the size of this field increases.
This interplay between complex geometry, the continuous, and finite field geometry, the discrete, has been a very fruitful two-way street that allows the transfer of results from one context to the other.
I will describe how we may count the number of points over finite fields of certain character varieties and discuss the geometric implications of this computation. The varieties parametrize representations of the fundamental group of a Riemann surface and are related to the moduli space of Higgs bundles on a curve.