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):

(G. Faurot):

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