Research

My research interests are primarily in applying homological methods to commutative algebra and related areas. Some topics that I am interested in include differential graded methods in commutative algebra, the structure of free resolutions over local rings, extending results about complete intersections to Koszul complexes, and cohomological support, varieties. I am particularly enjoy studying how A∞ structures, algebraic operads, triangulated categories, and homotopical algebra can be used to gain insight on the structure of local rings.

Papers

1. Systems of Higher Homotopies and Koszul Homomorphisms - joint work with Kory Pollicove and Ryan Watson. In preparation, preliminary draft available upon request.
2. Homological Algebra of Koszul Complexes - Thesis expected Summer 2026, topics include the previous work as well as
   • complexity results for DG modules over a Koszul complex
   • Frobenius endomorphisms and generators for derived categories in positive characteristic