Research interests: I am interested in the theory of algebraic groups and group schemes. I have worked on various aspects of their structure and representation theory, mostly when the underlying field has prime characteristic.
Research interests: I am interested in the theory of algebraic groups and group schemes. I have worked on various aspects of their structure and representation theory, mostly when the underlying field has prime characteristic.
Research Articles
Steinberg quotients, Weyl characters, and Kazhdan-Lusztig polynomials, to appear in Trans. Amer. Math. Soc.
On Donkin's tilting module conjecture III: New generic lower bounds (with Christopher Bendel, Daniel Nakano, and Cornelius Pillen), to appear in J. Algebra
On Donkin's tilting module conjecture II: counterexamples (with Christopher Bendel, Daniel Nakano, and Cornelius Pillen), to appear in Compositio Mathematica.
On Donkin's tilting module conjecture I: Lowering the prime (with Christopher Bendel, Daniel Nakano, and Cornelius Pillen), Represent. Theory 26 (2022), 455–497.
Exotic t-structure for partial resolutions of the nilpotent cone (with Kei-Yuen Chan and Laura Rider).
The Steinberg quotient of a tilting character, Math. Z. 297 (2021), no. 3-4, 1733–1747.
On character formulas for simple and tilting modules, Advances in Mathematics 369(2020), 107172, 8 pp.
Counterexamples to the tilting and (p,r)-filtration conjectures (with Christopher Bendel, Daniel Nakano, and Cornelius Pillen), to appear in J. Reine Angew. Math. 767 (2020), 193–202.
On tensoring with the Steinberg representation (with Christopher Bendel, Daniel Nakano, and Cornelius Pillen), Transformation Groups 25 (2020), no. 4, 981–1008.
Unipotent elements and generalized exponential maps, Advances in Mathematics 333 (2018), pp. 463-496.
On $(p,r)$-filtrations and tilting modules, Proc. Amer. Math. Soc. 146 (2018), no. 5, pp. 1951-1961.
A Fock space model for decomposition numbers for quantum groups at roots of unity (with Martina Lanini and Arun Ram), to appear in Kyoto J. of Mathematics.
Varieties of $G_r$-summands in rational $G$-modules, Geometric and topological aspects of the representation theory of finite groups, 377-392, Springer Proc. Math. Stat., 242, Springer, Cham, 2018.
On the existence of mock injective modules for algebraic groups (with William Hardesty and Daniel Nakano), Bull. London Math. Soc. 49 (2017), no. 5, 806-817.
On liftings of projective indecomposable $G_{(1)}$-modules, J. Algebra 475 (2017), pp. 61-79 (Sandy Green memorial issue).
Springer isomorphisms in characteristic p, Transformation Groups 20 (2015), no. 4, pp. 1141-1153.
Exponentiation of commuting nilpotent varieties, Journal of Pure and Applied Algebra 219 (2015), no. 6, pp. 2206-2217.
On exponentiation and infinitesimal one-parameter subgroups of reductive groups, J. Algebra 385 (2013), pp. 14-26.
Support varieties for Frobenius kernels of classical groups, Journal of Pure and Applied Algebra 216 (2012), pp. 2657-2664.
Module invariants and blocks of finite group schemes, Bull. London Math. Soc. 45(1) (2013), pp. 213-224.