My research interests are in homological methods in commutative algebra. I study the structure of resolutions and how they trasfer across ring maps. This leads me to study differential-graded algebras and A-infinity algebras, cohomological operators, and their connections to Koszul duality. Of particular interest to me is A-infinity coalgebras and their applications in constructing resolutions via twisted tensor constructions. I am working on applying these tools to certain ring maps in positive characteristic.
Preprints:
" Higher Homotopies and A-infinity Modules" - Joint with Dorian Kalir and Ryan WatsonÂ
In progress, draft available upon request
Thesis Work (in progress)
My thesis will feature results from the following topics:
Generalizing systems of higher homotopies and the applications to Koszul homomorphisms
From joint work with Kalir and Watson
Derived hochschild cohomology of of quasi-complete intersection homomorphisms in positive characteristic via counital diagonal approximations