Events and Activities

Abstract: Cohen, Lenstra, and Martinet have given highly influential conjectures on the distribution of class groups of number fields, the finite abelian groups that control the factorization in number fields. Malle, using tabulation of class groups...

Abstract: Starting with the "Leibniz" formula for $\pi$

$ \pi/4 = 1 - 1/3 + 1/5 - 1/7 + \ldots$

the special values of Dirichlet L-functions have long been a source of fascination and frustration. From Euler's solution in 1734 of the Basel problem to...

Abstract: What are the slopes of periodic billiard paths in a regular polygon?

We will connect this question and others to:

        - cusps of thin groups,

        - curves on Hilbert modular varieties,

        - heights from Jacobians with real...

Abstract: To study the asymptotic behavior of orbits of a dynamical system, one can look at orbit closures or invariant measures. When the underlying system has a homogeneous structure, usually coming from a Lie group, with appropriate assumptions a...

Abstract: (Joint with Samuel Grushevsky, Gabriele Mondello, Riccardo Salvati Manni) We determine the maximal dimension of a compact subvariety of the moduli space of principally polarized abelian varieties $A_g$ for any value of g. For $g<16$ the dimension is $g-1$, while for $g \geq 16$, it is determined by the larged dimensional compact Shimura subvariety, which we determine. Our methods rely on deforming the boundary using special varieties, and functional transcendence theory.

Abstract: Ratner's landmark equidstribution results for unipotent flows have had dramatic applications in many mathematical areas. Recently there has been considerable progress in the long sought for goal of getting effective equidistribution...