The talk will start with some remarks on the role that zeta functions and Tuberian theorems have played in number theory in the last 180 years starting essentially with Dirichlet's proof of his Arithmetic Progression Theorem. The remainder of the talk will be devoted to giving a survey of recent applications of Tauberian theorems to counting arithmetic objects. 

Oscar Villareal will lead a discussion on the NTRU Prime paper.

In this talk, we will discuss Furstenberg correspondence principle, which connects ergodic theory and combinatorial number theory. 

A "critical" metric on a manifold is a metric which is critical for some natural geometric variational problem. Some important examples of critical metrics are Einstein metrics and extremal Kahler metrics, and such metrics typically come in families. I will discuss some aspects of the local theory of moduli spaces of critical metrics, and present some compactness results for critical metrics which say that, under certain geometric assumptions, a sequence of critical metrics has a subsequence which converges, in the Gromov-Hausdorff sense, to a singular space with orbifold singularities. I will also discuss some results regarding the reverse problem of desingularizing critical orbifolds to produce new examples of critical metrics on smooth manifolds.