Research Interests

I work in algebraic geometry, including its interactions with neighboring fields such as representation theory, topology, and combinatorics. Of particular interest to me is intersection theory, which is the modern approach to analyzing solutions to algebraic equations. Intersection theory is used in enumerative geometry (the counting of geometric figures having a given relation to some given figures); this is a classical subject that has had an exciting revival inspired from physics and leads to a new intersection ring called quantum cohomology. Solving problems in these areas often involves constructing appropriate moduli spaces of the geometric objects and constructing useful compactifications of these moduli spaces. I am also interested in flag varieties, Schubert varieties, and related degeneracy loci, which are related to representation theory and studied by combinatorial methods. Other varieties that can be studied by combinatorics are toric varieties, whose algebraic geometry can be used to count lattice points in polyhedra.

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Section 11: Mathematics