Research

My research interests are in representation theory, algebraic geometry, and arithmetic geometry. Some particular interests are:

• the geometric Langlands program
• D-modules
• deformation theory
• Hochschild (co)homology
• cohomology theories in positive and mixed characteristic
• Dieudonné modules
• modular representation theory

Publications

On the differentials of the Hochschild-Kostant-Rosenberg spectral sequence. arXiv:2410.01894

Dieudonné theory for n-smooth group schemes. (with C. Kothari) arXiv:2408.15333

Higher Congruences in Character Tables. (with N. Harman) arXiv:2402.02312

Twisting the infinitesimal site. International Mathematics Research Notices 2024:19, 2024, pp. 12904–12918. arXiv:2310.06029

Hochschild cohomology of differential operators in positive characteristic. Journal of Algebra 650, 2024, pp. 367-376. arXiv:2303.07373

Almost All Wreath Product Character Values are Divisible by Given Primes (with B. Dong, H. Graff, S. Rothstein, L. Vescovo) Algebraic Combinatorics 6:6, 2023, pp. 1519-1531. arXiv: 2210.07261

Quantization of restricted Lagrangian subvarieties in positive characteristic. Advances in Mathematics 410:108760, 2022. arXiv: 2106.09912

In Preparation

Cartier duality via Mittag-Leffler modules. (with D. Arinkin)

Undergraduate Publications

appendix to Projective hypersurfaces in tropical scheme theory I: the Macaulay ideal, by A. Fink, J. Giansiracusa, N. Giansiracusa. Res Math Sci 12:30, 2025. arXiv: 2405.16338 This open-access article may be downloaded from this link.

The Image of a Tropical Linear Space. Electronic Journal of Combinatorics 35:1, 2025. arXiv: 1808.02150

The Manickam-Miklós-Singhi Parameter of Graphs and Degree Sequences. (with Z. Király, N. Kulkarni, I. McMeeking) Egerváry Research Group, Budapest, Technical Report 2018-11, 2018. arXiv: 1808.05835

A Module-Theoretic Approach to Matroids. (with C. Crowley, N. Giansiracusa) Journal of Pure and Applied Algebra 224(2):894-916, 2020. arXiv: 1712.03440

Quantum State Transfer on Coronas. (with E. Ackelsberg, Z. Brehm, A. Chan, C. Tamon) Electronic Journal of Combinatorics 24:2, 2017. arXiv: 1605.05260

Laplacian State Transfer on Coronas. (with E. Ackelsberg, Z. Brehm, A. Chan, C. Tamon) Linear Algebra and Its Applications 506:154-167, 2016. arXiv: 1508.05458

Videos of some talks

“Twisting the infinitesimal site.”

• “Gone Fishing” Poisson Geometry, 2024 April 13. Watch a video of this talk.

“Quantization of restricted Lagrangian subvarieties in positive characteristic.”

• “Gone Fishing” Poisson Geometry, 2023 March 16. Watch a video of this talk.