My research interests lie in algebraic geometry and algebraic topology, with particular emphasis on derived algebraic geometry, motivic homotopy theory, and higher algebra. I am also interested in their connections with symplectic and enumerative geometry.
Linear Koszul duality
This project develops a derived-geometric approach to linear Koszul duality, which gives a derived equivalence between the affine cone of a perfect complex and its shifted dual. The central problem is to realize the duality through Fourier–Mukai kernels and to compare the resulting equivalence with the construction of Mirković and Riche. Further connections with Fourier–Sato transforms and Kashiwara’s Fourier isomorphism are also being investigated.
Flop of derived Grassmann
This project studies derived Grassmannians associated with perfect complexes of virtual rank zero. It constructs Fourier–Mukai functors that realize the flop-flop-equals-twist phenomenon over arbitrary commutative rings, extending the Grassmannian-flop equivalences and twists introduced by Will Donovan and Ed Segal. Further results include the sphericality of the elementary flag functors, a natural flop–twist comparison, categorical Mackey relations, and their K-theoretic counterparts.
The rank-zero construction applies directly to Brill–Noether spaces of curves, where it produces spherical functors and recursive relations along the Brill–Noether tower. Related applications to moduli spaces of stable sheaves on K3 surfaces are currently under investigation.