Research

Publications and Preprints 

Note: the versions here may differ mildly from the arXiv versions. 

16. A Langlands dual realization of coherent sheaves on the nilpotent cone, with Harrison Chen, arXiv:2310.10539. 

15.  Semi-infinite parabolic IC sheaf, with Sergey Lysenko, arXiv:2310.06386.

14. On local geometric Langlands in positive characteristic,  RIMS Kokyuroku (2023).

13. Coulomb branches of noncotangent type, with Alexander Braverman, Michael Finkelberg, Sam Raskin, and Roman Travkin (with appendices by Gurbir Dhillon and Theo      Johnson-Freyd), arXiv:2201.09475.

12. The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras, arXiv:2109.12698. 

11. Steinberg--Whittaker localization and affine Harish-Chandra bimodules, with Justin Campbell, arXiv:2108.02806.

10. Localization for affine W-algebras, with Sam Raskin, Advances in Mathematics (2023). 

9. Fundamental local equivalences in quantum geometric Langlands, with Justin Campbell and Sam Raskin, Compositio Mathematica (2021). 

8. Semi-infinite cohomology and the linkage principle for W-algebras. Advances in Mathematics (2021). 

7. The tamely ramified fundamental local equivalence at integral level, with Justin Campbell, results superseded by no. 9 above, arXiv:1907.03204v1. 

6. Face of highest weight modules and the universal Weyl polyhedron, with Apoorva Khare. Advances in Mathematics (2017).

5. Bernstein--Gelfand--Gelfand resolutions and the constructible t-structure, Journal of Algebra (2022).

4. The weights of simple modules in Category O for Kac--Moody algebras, with Apoorva Khare, Journal of Algebra (2022). 

3. The Weyl--Kac weight formula, with Apoorva Khare. Seminaire Lotharingien de Combinatoire  (2017).

2. Opers, canonical forms, and the crystal raising operator. 

1. Extensions of Verma modules in dihedral Category O, with Visu Makam, arXiv:1712.05299.

Thesis

Geometric representations of W-algebras and applications to the quantum Langlands correspondence.

Expository Writing 

3. An informal introduction to categorical representation theory and the local geometric Langlands program, to appear in Journal of IISC. 

2. Proof of the Hard Lefschetz theorem, with Oscar Kivinen. Introduction to Soergel Bimodules, Springer RSME series.

1. Math 123: Lectures Notes and Homework Problems, with Levent Alpoge and Dennis Gaitsgory, AMS Open Math Notes.