The area of my work is algebraic geometry, which is the study of geometric shapes which are defined by polynomial equations. These shapes are called algebraic varieties.
I am mostly interested in:
- Fano varieties (which are the algebraic varieties with positive curvature) and their moduli spaces;
- toric varieties (which are algebraic varieties which can be constructed in a combinatorial way from polytopes and fans of cones);
- deformation theory (which is the study of how algebraic varieties deform when one perturbs their equations);
- Gromov-Witten theory (which enumerates/counts curves inside algebraic varieties).
