Research Interests: My research involves bringing together methods and results from algebraic geometry, algebraic groups, representation theory and convex geometry. In particular, my work involves drawing a connection between two areas of algebraic geometry: spherical varieties and Okounkov bodies. The current direction of my research is to investigate the geometry of spherical varieties using tools from the theory of Okounkov bodies. A central motivation in my research program has been to investigate how intersection theory on spherical varieties can be understood combinatorially.
Research Topics: Algebraic geometry, especially group actions on varieties; in particular, spherical varieties, Okounkov bodies and convex geometry, toric varieties, flag varieties, Schubert varieties and more generally Borel orbit closures in spherical varieties, intersection theory on spherical varieties, tropical geometry