Seminars Sorted by Series

I will give an overview of recent progress in random multiplicative functions (random models for multiplicative functions) and their connection to the study of the Fyodorov-Hiary-Keating conjecture and Polya's question on nonnegative character sums...

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 set of positive integer points of the celebrated Markov surface admits the structure of a 3-regular tree. My objective in this talk is to unveil a similar phenomenon for Mordell-Schinzel surfaces; namely that the set of positive integer points...

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...

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This is the opening talk of a learning seminar on geometric representation theory. The final goal of the seminar is to understand Bezrukavnikov's paper giving geometric realizations of the affine Hecke algebra, but we shall work through other topics...

We briefly review combinatorics and algebraic representation of reductive groups: root systems, Weyl groups and (extended) affine Weyl groups, weight spaces, and classification of irreducible representations in terms of highest weights. We define...

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...