Schedule of talks:

Abstracts

(B. Liu): Kleinian groups are discrete isometry subgroup of hyperbolic spaces. The action on the spaces is quite related to the geometry and dynamics of the quotient manifolds. I will introduce Kleinian groups of divergence type, which is equipped with nice dynamical features. Furthermore, if the group is a subgroup of a lattice, we show that the divergence type implies that random walks on the Schreier graph associated with the group is recurrent. The main ingredient is a connections among orbit counting of the group action on hyperbolic spaces, the volume growth rate of the quotient manifolds, and the growth rate of the Schreier graph.

(Y. Jing): A central problem in additive combinatorics is to understand how the size of a sumset (or product set) compares to the size of the original set, and to describe the underlying structure when this "doubling" is small. In this talk, I will survey some classical results in the area and discuss recent developments in the setting of compact Lie groups, based on joint work with Chieu-Minh Tran and Simon Machado.

(R. Haburcak): Algebraic curves (Riemann surfaces), and their moduli space, are classical objects of interest in geometry, algebra, and number theory. Given a curve, it is natural to ask how can we put it into projective space? The study of maps from curves to project space is Brill-Noether theory, also called a "representation theory for curves". We'll give an overview of how Brill-Noether theory impacts other properties of curves and highlight recent developments.

(M. Lipnowski): Given (finitely many) balls in a metric space, do they admit a common intersection point? An efficient solution to this problem would be broadly applicable to questions in computational topology. We discuss the intersecting balls problem in the context of metric spaces having "thin triangles" and describe one attempt to solve this problem for symmetric spaces.

(G. Faurot): The study of $C^*$-algebras is frequently referred to as "noncommutative topology," as Gelfand duality shows that any (unital) commutative $C^*$-algebras arises as the algebra of continuous functions on a compact Hausdorff space. As a result, many techniques and properties used to study $C^*$-algebras are generalized from topology. One such example is nuclear dimension, which is a noncommutative analogue of covering dimension. In this talk, we will discuss bounds on the nuclear dimension of graph $C^*$-algebras, whose properties are closely related to their underlying graph structure. We will also discuss the related regularity property of $\mathcal{Z}$-stability and its application to graph $C^*$-algebras. Portions of this work is joint with Samuel Evington and Christopher Schafhauser.

This page is maintained by Dave Anderson.