Cohomological Hall algebras
CoHAs encode extension data in categories of geometric objects. I study their structure, commutativity and degenerations, and cohomological integrality theorems for symmetric stacks and reductive group representations.
Research programme
Geometry, representations and BPS invariants
My research explores algebraic structures arising from the geometry and cohomology of moduli spaces and stacks.
Overview
I work in geometric representation theory, at the interface of algebraic geometry, topology and representation theory. My research focuses on cohomological Hall algebras (CoHAs), BPS Lie algebras, moduli spaces of sheaves and representations, and the interplay between these structures and Calabi–Yau geometry.
A central goal is to understand how the geometry of moduli stacks gives rise to algebraic structures and decompositions of their cohomology. I use techniques involving perverse sheaves, mixed Hodge modules, Donaldson–Thomas theory and algebraic stacks.
Four directions
Research themes
BPS cohomology and Lie algebras
BPS structures link moduli-space cohomology to Lie-theoretic invariants, PBW-type theorems and generalized Kac–Moody algebras. A recurring case is that of 2-Calabi–Yau categories and related moduli stacks.
Moduli spaces and nonabelian Hodge theory
I investigate cohomological and representation-theoretic structures on moduli stacks of sheaves, Higgs bundles and local systems, particularly comparisons arising from nonabelian Hodge theory.
Quivers, perverse sheaves and counting
Quiver representations provide a model for understanding representation-theoretic constructions, cuspidal functions, Lusztig sheaves, Kac polynomials and questions about quiver varieties.
ANR JCJC · 2027–2031
ReSCoS
My ANR JCJC project supports a research programme in geometric representation theory, with a particular focus on cohomological Hall algebras, BPS invariants and moduli spaces.
Project website → · Opportunities for students and postdocs →
Research output