Research

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My research interests are homological algebra, homotopical algebra, and noncommutative geometry.

Specifically, I am interested in various constructions and properties of Hochschild and cyclic homology, and connect them to other areas, such as noncommutative geometry, (derived) algebraic geometry, and string topology.

I am also interested in the applications of algebra to artificial intelligence (AI).

Publications and Preprints

• Curved Koszul duality and cyclic (co)homology, Preprint (2021), submitted.
• Hodge decomposition of string topology (with Yu. Berest and A. C. Ramadoss), Forum Math. Sigma. 9 (2021), e33.
• Cyclic pairings and derived Poisson structures (with A. C. Ramadoss), New York J. Math. 25 (2019), 1-44.
• Dual Hodge decompositions and derived Poisson brackets (with Yu. Berest and A. C. Ramadoss), Selecta Math. (N.S.), 23 (2017), 2029--2070.