Research Interests
I am a mathematician who works in the field of algebraic geometry. I am currently working on the following topics.
- Characteristic classes of singular spaces:
Singularity theory is at the crossroads of multiple mathematical disciplines. It is related to algebraic geometry, algebraic topology, combinatorics, mathematical physics, PDE, etc. Given a singular space, there exists canonically defined notable elements in its (co)homology groups. These elements delicately reflect properties of the given singular space.
- Free divisors:
These are a class of singular spaces. The general theory of free divisors has applications on the study of hyperplane arrangements. Moreover, the Hodge-theoretic aspects of free divisors are interesting.
- Discriminants:
They often arise from the versal deformation of singularities, or from the representation of certain algebraic groups. Discriminants are often free divisors.
Click here for my current CV.