Research

Publications and Preprints

1. Relative Langlands duality of Hitchin systems, in preparation, 2024.

   • An introduction to some of the ideas were presented at the ICMS conference Gauge fields in arithmetic, topology, and physics, in Edinburgh, April 2024. A recording of the presentation can be found here.

2. Relative (BBB)-branes on the Hitchin moduli stack, (with Emilio Franco), in preparation, 2024.

3. Some singular examples of relative Langlands duality, (with Akshay Venkatesh), draft updated May 10th, 2024. 

   • We develop the notion of automorphic periods and L-functions attached to certain singular varieties in order to restore the Langlands duality underlying Ginzburg's integral of the SL3 adjoint L-function and Garrett's triple product integral. In an appendix we record well behaved smooth examples of automorphic period/L-function duality in the sense of BZSV. 

4. Relative Langlands duality of toric periods, draft updated May 10th, 2024. 

   • In this companion paper to Some singular examples of relative Langlands duality, we study in finer detail the BZSV automorphic period/L-function duality in the case when the group is a torus. Such details include the regularization and interpretation of nonconvergent periods, and extensions of duality statements to disconnected stabilizers / Deligne--Mumford quotients. 

5. Generic extensions and generic polynomials for linear algebraic groups, (with J.T. Ferrara and Liam Mazurowski), Journal of Algebra Volume 461, 2016.  

   • A generic extension of a field K with a group G is, roughly speaking, a moduli space of Galois extensions of K with Galois group G. In this article we construct such generic extensions for certain groups of Lie type in characteristic p.