I work in homological algebra and homotopy theory.
My research focuses on applications of homotopy-theoretic methods to problems in abstract algebra, algebraic geometry, and certain areas of mathematical physics.
- "Kontsevich's graph complex, GRT, and the deformation complex of the sheaf of polyvector fields"
(with V. Dolgushev and T. Willwacher)
Annals of Mathematics vol. 182 (2015) 855-943.
- "Homotopy moment maps"
(with M. Callies, Y. Frégier, and M. Zambon)
Advances in Mathematics vol. 303 (2016) 954-1043.
- "An explicit model for the homotopy theory of finite type Lie n-algebras"
Algebraic and Geometric Topology vol. 20 (2020) 1371-1429.
- "On the homotopy theory for Lie ∞-groupoids, with an application to integrating L∞-algebras"
(with C. Zhu)
Algebraic and Geometric Topology vol. 20 (2020) 1127-1219.
- "The cohomology of the full directed graph complex"
(with V. Dolgushev)
Algebras and Representation Theory vol. 23 (2020) 917-961.
- "Which homotopy algebras come from transfer?"
(with M. Markl)
Proceedings of the American Mathematical Society (2021) To appear in print, DOI: 10.1090/proc/15710.