Research

My research focus is geometric representation theory, but I'm more broadly interested in its connections to algebraic geometry, mathematical physics, the Langlands program, and homotopy theory.

Research Articles

• Functoriality of Coulomb Branches (with Ben Webster) - Talk

• Quantization of the Universal Centralizer and Central D-modules (with Victor Ginzburg) - Talk

• The Cotangent Bundle of G/Uₚ and Kostant-Whittaker Descent

• Differential Operators on the Base Affine Space of SLₙ and Quantized Coulomb Branches (with Harold Williams) - Talk

• Proof of the Ginzburg-Kazhdan Conjecture - (Talk | Notes)

• Classification of Nondegenerate G-Categories - (Slides)

• The Universal Category 𝒪 and the Gelfand-Graev Action

• The Coarse Quotient for Affine Weyl Groups and Pseudo-reflection Groups

Undergraduate Research

• New Results on Semipositive Matrices  (with Jonathan Dorsey, Charles Johnson, and Morrison Turnansky)

• Linear Preservers of Semipositive Matrices  (with Jonathan Dorsey, Nathaniel Jacobson, Charles Johnson, and Morrison Turnansky)