Research Interests

My main interest within mathematics is combinatorics, especially its relationship with other areas of mathematics such as commutative algebra, algebraic geometry, algebraic topology, and representation theory. For instance, I solved some previously intractable combinatorial problems concerning simplicial complexes and convex polytopes by associating a certain commutative ring with a simplicial complex and then using techniques of commutative and homological algebra to analyze the structure of this ring. Similarly, I proved a number-theoretic conjecture of Erdos and Moser by applying some deep theorems in algebraic geometry to the cohomology ring of a certain algebraic variety.

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Section 11: Mathematics