My research is focused on different methods of understanding singularities in commutative algebra. In particular, my interests include multiplicities, convex geometric methods, symbolic powers, homological methods and connections to combinatorics.
Partial Betti splittings with applications to binomial edge ideals (with Adam Van Tuyl and A.V. Jayanthan)
Collectanea Mathematica (2026). [arxiv]
We introduce the notion of a partial betti splitting for graded ideals. We use this to obtain interesting results about the Betti numbers of binomial edge ideals.
The multiplicity sequence of monomial ideals (with Sudipta Das and Jonathan Montaño)
(submitted). [arxiv]
We give a formula for the multiplicity sequence of a monomial ideal in terms of mixed volumes of polytopes constructed from its Newton polyhedron.
Polynomial interpolation and the Waldschmidt constant of points in projective space (with Tài Huy Hà)
(submitted). [arxiv]
We establish Chudnovsky's Conjecture and Demailly's Conjecture for any finite set of points in projective space.