Richard P. Stanley

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.