I work in the field of complex algebraic geometry. Here is what I like most:
- Derived categories: I am interested in the construction of semiorthogonal decompositions, and their role in the study of derived categories of Fano and Calabi—Yau manifolds.
- Homogeneous varieties and vector bundles: Many interesting examples of Fano and Calabi—Yau varieties arise as zero loci of sections of homogeneous vector bundles on generalized Grassmannians and flags. Most of the problems I’m working on fall in this class.
- Gauged linear sigma models: In theoretical physics, there is an interesting correspondence between zero loci of sections of homogeneous vector bundles and certain two-dimensional supersymmetric field theories. In particular, phase transitions of such models provide candidate derived equivalent pairs of varieties in algebraic geometry.
