## Research Interests

Representation theory, with an emphasis on geometric and diagrammatic techniques.

Some objects/topics that appear in my research:

- perverse sheaves
- Hecke category in its various incarnations (parity sheaves on Kac-Moody flag varieties, Soergel bimodules, Braden–MacPherson sheaves on Bruhat moment graphs, Elias-Williamson diagrammatic category)
- modular representation theory of reductive groups
- diagrammatic presentation for various categories in representation theory
- link homology (Khovanov, Khovanov-Rozansky, HOMFLYPT)

## Papers

Most of my papers are available on the arXiv e-print server. You can also find me on Google Scholar.

### In preparation

- [8] (with M. Khovanov) A diagrammatic categorification of the 0-Hecke algebra

### Preprints

- [6] (with M. Hogancamp) Ext-enhanced monoidal Koszul duality for GL_2
- [3] (with P. N. Achar, S. Riche, and G. Williamson) Free-monodromic mixed tilting sheaves on flag varieties
- [2] Modular Koszul duality for Soergel bimodules
- [1] Mixed perverse sheaves on moment graphs

### Published / to appear

- [5] On monoidal Koszul duality for the Hecke category, to appear in the Proceedings of the XXII Latin American Algebra Colloquium,
*Revista Colombiana de Matemática* - [4] (with P. N. Achar, S. Riche, and G. Williamson) Koszul duality for Kac–Moody groups and characters of tilting modules,
*J. Amer. Math. Soc.***32**(2019), 261–310. DOI

### Book to appear

- [7] (with B. Elias, U. Thiel, G. Williamson) Introduction to Soergel bimodules (with contribution from 37 other authors), to appear in the RSME Springer Series

### Other mathematical writing

- [0] Ph.D. Thesis, Stanford University, 2017 (available in paper form as [1] and [2])

## Collaborators

Pramod N. Achar, Ben Elias, Matthew Hogancamp, Lars Thorge Jensen, Mikhail Khovanov, Simon Riche, Ulrich Thiel, Geordie Williamson

## Videos

Modular Koszul duality for Kac–Moody groups, talk at Perimeter Institute (November 2017)## Research done as an undergrad

Until early grad school, I thought I might want to do number theory. I wrote my undergraduate thesis at Princeton [-1] under Peter Sarnak. Even earlier, in summer 2009, I worked on [-2] for the fractal REU at UConn.

- [-1]
*A note on Riemann surfaces of large systole*,*J. Ramanujan Math. Soc.***28**(3): 359–377 (2013). MR3113388. - [-2] (with G. Stadnyk and B. Steinhurst)
*Modified Hanoi Towers Groups and Limit Spaces*,*International Journal of Algebra and Computation***21**(6): 867–887 (2011). MR2847514.