I work in the fields of algebraic geometry and representation theory. More specifically, my research is focused on problems in Donaldson-Thomas theory for resolutions of singularities, such as those appearing in the minimal model program. The goal of DT theory is to extract invariants from certain moduli spaces of objects in the derived category of a variety. These spaces are often complicated beasts, which need to be tamed before one can make any substantial progress. To do this, we I use tools from various adjacent areas:
- The theory of stability conditions, which breaks down moduli spaces into more manageable strata,
- Tilting theory, which relates different moduli spaces to one another (i.e. complicated ones to simpler ones),
- Noncommutative deformation theory, which allows one to leverage various techniques from algebra and physics.
The goal of my research is therefore to develop the parts of these areas that improve our understanding of some of the moduli spaces we encounter in the MMP.