Research
My research is primarily concerned with the local Langlands correspondence. In particular, my interests include:
Epipelagic representations of p-adic groups and their related Langlands parameters, particularly for small p
Arithmetic invariant theory
Exceptional groups and their representations
Papers
On input and Langlands parameters for epipelagic representations, Representation Theory 28 (2024), pp. 90 - 111.
Stable vectors in dual Vinberg representations of F4, Transformation Groups (2022).
A nonabelian Fourier transform for tempered unipotent representations, with Anne-Marie Aubert and Dan Ciubotaru, accepted for publication in Compositio Mathematica.
From p-modular to p-adic Langlands correspondences for U(1,1): deformations in the non-supercuspidal case (with Ramla Abdellatif, Agnes David, and Hanneke Wiersema), accepted for publication in Women in Numbers Europe III: Research Directions in Number Theory. Edited by Alina Cojocaru, Sorina Ionica and Elisa Lorenzo García. Association for Women in Mathematics Series, Springer.
On central extensions and simply laced Lie algebras, Journal of Algebra, Vol. 568 (2021).
E8 and the average size of the 3-Selmer group of the Jacobian of a pointed genus-2 curve (with Jack Thorne), Proceedings of the London Mathematical Society, Vol. 122, Issue 5 (2021).
On the arithmetic of simple singularities of type E (with Jack Thorne), Research in Number Theory 4 (2018), no.2.
Stable vectors in Moy-Prasad filtrations (with Jessica Fintzen), Compositio Mathematica, Vol. 153, Issue 2 (2017), pp. 358-372.
On the local Langlands correspondence: new examples from the epipelagic zone, PhD thesis (Boston College), 2016