Research

My work is centered around the field of Geometric Representation Theory, which involves aspects of Representation Theory, Algebraic Geometry, Topology, and Mathematical Physics. Some particular interests include D-modules, topological field theory, skein modules, and (higher) categorical structures. 

I am supported by NSF grant DMS-2202363, The Langlands Program for 3-manifolds. 

Published/Accepted:

• The finiteness conjecture for skein modules (joint with David Jordan and Pavel Safronov), Inventiones Mathematicae (2022). arXiv:1908.05233 

• The Jordan-Chevalley decomposition for G-bundles on elliptic curves (joint with Dragos Fratila and Penghui Li) Representation Theory (ERT), 2022. arXiv:2007.03229 

• Projective generators for equivariant D-modules (joint with Gwyn Bellamy and Sam Raskin) Transformation Groups (2022) arXiv: 1905.05073. 

• Highest Weights for Categorical Representations (joint with David Ben-Zvi and Hendrik Orem) International Mathematics Research Notices (2018) arXiv:1608.08273 

• Generalized Springer Theory for D-modules on a Reductive Lie Algebra, Selecta Mathematica, New Series (2018) 

• The Character Field Theory and Homology of Character Varieties (joint with David Ben-Zvi and David Nadler) Mathematical Research Letters (2019) arXiv:1705.04266 

• The Arf-Brown TQFT of Pin- Surfaces (joint with Arun Debray) Topology and Quantum Theory in Interaction (Contemporary Mathematics) (2018) arXiv:1803.11183 

• Spin Hurwitz numbers and topological quantum field theory Geometry & Topology 20-4 (2016), 1859–1907.

Preprints: 

• Deformation Quantization and Perverse Sheaves (joint with Pavel Safronov), arXiv: 2312.07595

• Quantum Character Theory (joint with David Jordan and Monica Vazirani), arXiv: 2309.03117

• A Derived Decomposition for Equivariant D-modules, arXiv:1705.04297 

• Symmetries of categorical representations and the quantum Ngˆo action (joint with David Ben-Zvi) arXiv:1712.01963 

Mini-courses:

• The Springer Correspondence (an Introduction to Geometric Representation Theory). LMS Algebra School, September 2020