web stats

About Me

I am an NSF and an EPSRC Postdoctoral Fellow at Cambridge and a Research Fellow in Homerton College, Cambridge. My NSF mentor is Prof. Mark Gross. I received my PhD in 2014 at the University of Pennsylvania, advised by Prof. Ron Donagi. I did my undergraduate studies at the University of Georgia.

My primary research interests are in mirror symmetry and algebraic geometry. Mirror symmetry is a conjecture inspired by a duality in string theory called T-duality that allows one to encode symplectic information about one space into the algebraic geometry of another and vice versa. I study this duality in various ways as well as implications it may have for number theory.

If one studies mirror symmetry for a symplectic manifold, its mirror is a Landau-Ginzburg model, which is a triplet of data: an algebraic space (or variety), a group acting on it, and a regular function on this space that is invariant with respect to the group. Here, the symplectic geometry of the manifold you started with is encapsulated in the algebro-geometric data of the singularity defined by this function.

The Landau-Ginzburg model is oftentimes very malleable and provides a geometric description for many algebraic objects. In the past, I used it to give a unification of various constructions of mirrors to subvarieties in toric varieties. I lately have been researching its homological and enumerative properties. I am very interested in studying Landau-Ginzburg models in the context of global mirror symmetry.