Summary of research interests

My research interests are focused on understanding aspects of symmetry in mathematical models of string theory. More specifically, I am interested in mirror symmetry constructions for (partial) flag varieties and their symplectic quotients, and the emergence of combinatorial and geometric representation theory in these constructions.

In my PhD thesis I investigated ways in which mirror symmetry manifests in the geometry of partial flag varieties and symplectic quotients of these spaces, known as weight varieties. My thesis comprised of two parts: the first part focused on mirror constructions for weight varieties; the second part focused on the appearance of combinatorial representation-theoretic objects, known as Kashiwara crystals, in these mirror constructions for weight varieties.

Publications

• Crystals in Mirror Symmetry (in preparation)
• Soergel Bimodules and the Shape of Bruhat Intervals (with W. Slofstra) (in preparation)
• Crystals and Mirror Constructions for Quotients (PhD Thesis)
• Representations of Quiver Hecke Algebras via Lyndon Bases (with D. Hill, D. Mondragon), Journal Pure and Applied Algebra Vol. 216, 5, May 2012, p. 1052-1079