School of Mathematics
A basic but difficult question in the analytic theory of automorphic forms is: given a reductive group G and a representation r of its L-group, how many automorphic representations of bounded analytic conductor are there? In this talk I will present an answer to this question in the case that G is a torus over a number field.
Let F be a family of subsets over a domain X that is closed under taking intersections. Such structures are abundant in various fields of mathematics such as topology, algebra, analysis, and more. In this talk we will view these objects through the lens of convexity.
We will focus on an abstraction of the notion of weak epsilon nets:
given a distribution on the domain X and epsilon>0,
a weak epsilon net for F is a set of points that intersects any set in F with measure at least epsilon.
We will hear from two passionate creators of successful mentoring programs in math for high school kids in educationally challenged environments. They will give back-to-back talks about their experiences and educational insights.
Ribbon graphs capture the topology of open Riemann surfaces in an elementary combinatorial form. One can hope this is the first step toward a general theory for open symplectic manifolds such as Stein manifolds. We will discuss progress toward such a higher dimensional theory (joint work with Alvarez-Gavela, Eliashberg, and Starkston), and in particular, what kind of topological spaces might generalize graphs. We will also discuss applications to the calculation of symplectic invariants.
study periods of automorphic forms of unitary groups that show
up in Ichino-Ikeda conjecture. In this talk, I will report on the
present state of the Jacquet-Rallis trace formula. Then I will
discuss the problem of the spectral expansion. (joint work with Michal