Events and Activities

Over the past 50 years, cryptographers have constructed a number of surprising and important primitives like public-key encryption, which allows strangers to communicate privately even if eavesdroppers hear everything they say. However, there are...

I will prove Gromov's conjecture that every 3-manifold of positive scalar curvature contains a short closed geodesic. The proof uses Min-Max theory of minimal surfaces and a combinatorial version of mean curvature flow. Time permitting, I will...

In 2011 Bourgain and Rudnick showed that if $\gamma$ is a curve of non-vanishing curvature on the 2d standard flat torus, then there are no Laplace eigenfunctions of arbitrarily large eigenvalues containing $\gamma$ in their nodal set. We show that...

I'll discuss our attempts to model problems of bio molecular assembly using simple geometric constructions. We contrast how nature makes polyhedra with classical constructions. The issue that really bothers me is this: biomolecular codes are...

In this talk I will introduce a bi-\bar{Q}-structure on Shimura varieties, propose a hyperbolic analytic subspace conjecture (analogue of Wüstholz’s analytic subgroup theorem in this context), and explain its consequence on quadratic relations...

I will report on joint work in progress with Tim Browning and Ritabrata Munshi, concerning the use of the circle method to count rational points on a particular cubic hypersurface in six variables. This problem lies at the square-root barrier, and I...