Research Interests

These are the fields I am currently working on:

Derived categories and semiorthogonal decompositions: Exceptional collections, semiorthogonal decompositions, and mutations provide powerful tools to understand derived categories of coherent sheaves and categorical resolutions of singularities, and to investigate the geometric information that they carry.
Birational equivalences, K-equivalence, and the DK conjecture: While the derived category is known to be an invariant up to isomorphism for smooth Fano and general type varieties, its behavior as a birational invariant in broader settings remains the subject of open conjectures. In particular, there is substantial evidence suggesting that certain birational transformations, known as K-equivalences, should induce equivalences at the level of derived categories.
Gauged linear sigma models, phase transitions, mathematical physics: In physics, gauged linear sigma models are supersymmetric gauge theories that exhibit multiple phases. Unlike the original abelian models, non-abelian GLSMs can have several geometric phases, each corresponding to the geometry of a smooth projective variety. Conjecturally, the physical relationship between these phases is reflected mathematically by Fourier–Mukai functors inducing equivalences, or embeddings, between the derived categories of the associated varieties.
Varieties with two projective bundle structures: The classification of simple K-equivalences, i.e., K-equivalences which are resolved by single smooth blowups, is closely related to the classification of special Fano varieties called roofs. These are varieties of Picard rank two, whose extremal contractions are projective bundles, equipped with a line bundle which restricts to the relative hyperplane bundle on the fibers of each contraction. Despite these are rather restrictive conditions, completing the latter classification is still an open problem.