My research interest is in derived categories and hyperkähler manifolds. In particular, I am interested in finding more derived equivalences between generalized Kummer varieties and find some derived invariant lattices. I am currently thinking about the D-equivalence conjecture about generalized Kummer varieties.
Publication and preprints:
[1] Lifting derived equivalences of abelian surfaces to generalized Kummer varieties. Electronic preprint, arXiv: 2507.11358, submitted.
In this article, we study the G-autoequivalences of the derived category D^b_G(A) of G-equivariant objects for an abelian variety A with G being a finite subgroup of Pic^0(A). We provide a result analogue to Orlov's short exact sequence for derived equivalences of abelian varieties. It can be generalized to the derived equivalences of abelian varieties for a same G in general. Furthermore, we find derived equivalences of generalized Kummer varieties by lifting derived equivalences of abelian surfaces using the G-equivariant version of Orlov's short exact sequence and some "splitting" propositions.
[2] Derived categories of generalized Kummer varieties: Extended Mukai vector. Electronic preprint, arXiv: 2507.16279.
We use the extended Mukai vectors for hyper-Kähler manifolds to investigate the derived equivalences of the hyper-Kähler manifolds deformation equivalent to generalized Kummer varieties. Inspired by the idea for hyper-Kähler manifolds of K3[n]-type, we obtain an integral lattice which is proved to be invariant under the derived equivalences of generalized Kummer type varieties. Such results and applications are described using derived monodromy groups.
In preparation:
New derived equivalences of generalized Kummer varieties