Research Statement: Combinatorial Structures in Pure and Applied Mathematics

I am a combinatorialist with diverse interests. The power of combinatorics derives from the wide applicability of its methods. Discrete structures arise throughout mathematics and science, yet all too often combinatorics is unnecessarily done in isolation. I aim to bridge the gap between combinatorics and other fields through collaborations with mathematicians and scientists from varied disciplines. In pure mathematics, my projects have focused on topics in algebraic geometry, representation theory, commutative algebra and combinatorics. In interdisciplinary work, I apply combinatorics in the service of neuroscience, population genetics and ecology, with connections to computer science.