# Past Events

We will discuss recent progress and resolution of a series of conjectures by Mazur, Rubin, Stein on the statistical behavior of modular symbols in order to understand the central values of twists of L-functions of elliptic curves. These values have been the object of extensive studies in…

The discovery of the Jones polynomial in the early 80's was the beginning of “quantum topology": the introduction of various invariants which, in one sense or another, arise from quantum mechanics and quantum field theory. There are many mathematical constructions…

The α-Lipschitz minorant of a function is the greatest α-Lipschitz function dominated pointwise by the function, should such a function exist. I will discuss this construction when the function is a sample path of a (2-sided) Lévy process. The contact set is the random set of times when the…

Let (*M*, ω) be a closed symplectic manifold. Consider a closed symplectic submanifold *D* whose homology class is a positive multiple of the Poincare dual of [ω]. The complement of *D* can be given the structure of a Liouville manifold, with skeleton *S…*

We show that the second moment for the number of integral points on elliptic curves over

Q is bounded. The main new ingredient in our proof is an upper bound on the number of

integral points on an affine integral Weierstrass model of an elliptic curve depending only on

the rank of…