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
Math 1116: Excursions in Mathematics - Online Lessons