Seminars Sorted by Series

We propose and study a new arithmetic invariant of non-hyperelliptic genus-4 curves: a canonical “quadratic” point on the Jacobian, defined by the two natural degree-2 maps to projective lines. Building on Xue’s result, that this point is...

Borel proved that every holomorphic map from a product of punctured unit discs to a complex Shimura variety extends to a map from a product of discs to its Bailey-Borel compactification. In joint work with Oswal, Zhu, and Patel, we proved a p-adic...

It is possible to form "theta series" in other geometric contexts, e.g. for counting problems involving abelian varieties. It is expected that these theta series again have additional automorphic symmetry.


I will explain some “near-central”...

In this talk, I will present recent work on the intersection theory of modular correspondences. Specifically, we study the intersection numbers of modular correspondences of square-free level, focusing both on the nonsingular intersections and the...

In this talk, we continue to discuss the intersection of modular correspondences but on the self-product of two Shimura curves. This is partially motivated by a classical work of Kudla-Rapoport for the single Shimura curve case and by the self...

I will report on joint work with Aurel Page on a number/representation theoretic approach to the question "Can you hear the shape of a drum". We use quaternion algebras over number fields to construct pairs of manifolds that "sound the same", but...

The main source for the works of Archimedes is a medieval manuscript, written originally around in 975 CE and then erased and covered with a prayerbook in the year 1229. Briefly studied in 1906, the full contents of the manuscripts were finally...

In this talk, I will explain how the Ruelle invariant of a symplectomorphism and the Ruelle invariant of a Reeb flow are related via the open book construction. As an application, I will construct examples of Reeb flows on the sphere that are...