My research to date has been in the study of semisimple Lie algebras, and more generally Kac–Moody algebras, and their representation theory. These areas include a rich interplay between methods and objects in algebra (irreducible representations, Demazure modules, tensor products,...), geometry (flag varieties, Schubert varieties, cohomology,...), and combinatorics (Weyl groups, characters, convex polytopes,...).
More specifically, a major portion of my work to date has focused on variations on the theme of branching problems, or restricting a representation of a Lie algebra to a distinguished subalgebra. These problems can naturally be studied via the reinterpretation and transfer of information between the associated algebraic, geometric, and combinatorial objects of interest.
Published Papers
Geometric invariant theory and stretched Kostka quasi-polynomials (with M. Besson and J. Kiers), International Mathematics Research Notices, vol. 2025, issue 5.
Irreducible components in Hochschild cohomology of flag varieties , Proceedings of the American Mathematical Society, vol. 153, Number 8 (3227--3240), 2025.
Components of V(ρ)⊗V(ρ) and dominant weight polyhedra for affine Kac--Moody Lie algebras (with S. Kumar), Transformation Groups, 2023.
Weight polytopes and saturation of Demazure characters (with M. Besson and J. Kiers), Mathematische Annalen, vol. 388 (4449--4486), 2024.
Root components for tensor product of affine Kac--Moody Lie algebras (with S. Kumar), Representation Theory (An electronic journal of the American Mathematical Society), vol. 26 (825--858), 2022.
Vertices of intersection polytopes and rays of generalized Kostka cones (with M. Besson and J. Kiers), Journal of Lie Theory, vol. 31, No. 4 (1055--1070), 2021.
Multiplicity in root components via Geometric Satake (with M. Besson and J. Kiers), Communications in Algebra, vol. 50, No. 6, 2022.
Preprints
Affine Demazure weight polytopes and twisted Bruhat orders (with M. Besson and J. Kiers), submitted.
Toward a Jacobson--Morozov theorem for Kac--Moody Lie algebras, arXiv.