Here is a summary of my research interests and some written materials.
- Derived and DG categories
- Fourier-Mukai transforms
- Moduli spaces
- Representations of quivers
Combinatorial generation of derived categories of GIT quotients
We can re-prove fullness of Kapranov's exceptional collections on grassmannians using combinatorial constructions. For quivers, we can also get generation results, however the resulting set of generators is pretty big. More details can be found in these lecture notes.