Research

I am interested in Galois representations, modular forms, algebraic groups, and p-adic analysis.

My papers and preprints:

Remarks on compatible systems of Galois representations over function fields. arXiv preprint.

Lifting G-valued Galois representations when \ell \neq p, joint with Jeremy Booher and Sean Cotner.

P-adic incomplete gamma functions and Artin-Hasse-type series, joint with Xiaojian Li, Jay Reiter, Napoleon Wang and Jin Yi (undergrad co-authors, accepted by p-Adic Numbers, Ultrametric Analysis and Applications).

A note on Galois representations valued in reductive groups with open image (accepted by Journal of Number Theory).

Congruences like Atkin’s for the partition function, joint with Scott Ahlgren and Patrick Allen (accepted by Transactions of the AMS).

Motivic Galois representations valued in spin groups, Journal de Theorie des Nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 197-221.

Potential automorphy of GSpin_{2n+1}-valued Galois representations, joint with Stefan Patrikis. Mathematische Zeitschrift. (2021).

Algebraic monodromy groups of G-valued \ell-adic Galois representations, Algebra Number theory, Vol.13, No.6, 1353-1394 (2019).

Action of intertwining operators on pseudospherical K-types, Pacific Journal of Mathematics, Vol. 286, No. 1, 2017.

Principal series representations of metaplectic groups, arXiv preprint (not intended for publication).