Events and Activities

Many geometric spaces carry natural collections of special submanifolds that encode their internal symmetries. Examples include abelian varieties and their sub-abelian varieties, locally symmetric spaces with their totally geodesic subspaces, period...

The Poisson summation conjecture of Braverman-Kazhdan, L. Lafforgue, Ngo, and Sakellaridis is an ambitious proposal to prove analytic properties of quite general Langlands L-functions using vast generalizations of the Poisson summation formula. In...

High-dimensional expanders (HDX) are a generalization of expander graphs which have seen various applications in coding theory, PCPs, pseudorandomness, derandomization, approximate sampling, and beyond. One technique for proving a complex is an HDX...

High-dimensional expanders (HDX) are a generalization of expander graphs which have seen various applications in coding theory, PCPs, pseudorandomness, derandomization, approximate sampling, and beyond. One technique for proving a complex is an HDX...

Since Hironaka's famous resolution of singularities in characteristics zero in 1964, it took about 40 years of intensive work of many mathematicians to simplify the method, describe it using conceptual tools and establish its functoriality. However...

We describe the obstruction to lift Frobenius on certain Shimura varieties and apply this to the theory of companion forms for classical modular forms (Gross, Coleman-Voloch, Faltings-Jordan) and also in higher dimension.

The study of Turán numbers of graphs and hypergraphs is a rich problem in extremal combinatorics. The Turán problem asks, given a fixed forbidden (hyper)graph F, what is the maximum number of edges in an F-free (hyper)graph in terms of the number of...

The study of Turán numbers of graphs and hypergraphs is a rich problem in extremal combinatorics. The Turán problem asks, given a fixed forbidden (hyper)graph F, what is the maximum number of edges in an F-free (hyper)graph in terms of the number of...

Ricci solitons are the self-similar solutions to the Ricci flow, which is the heat equation for Riemannian metrics, and they model singularity formation. We survey various estimates for Ricci solitons in dimension 4. This is mainly the work of...