Research

I am interested in algebraic number theory and representation theory. More specifically, I have worked on Galois representations, automorphic forms, reductive groups and their representations. I am currently working on proving the existence of formally smooth components of the \ell \neq p local deformation ring for Galois representations valued in arbitrary reductive groups (joint with Jeremy Booher). I like to think about analogues of representation-theoretic tools and ideas for Galois representations valued in arbitrary reductive groups, for example, Serre’s theory of complete reducibility.

My papers and preprints:

Congruences like Atkin’s for the partition function, joint with Scott Ahlgren and Patrick Allen.

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.

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