I study noncommutative and Poisson algebras from (symplectic) geometric, representation-theoretic, and cohomological points of view. In particular, I have developed new homology theories (such as Poisson-de Rham homology) for Poisson varieties and their quantizations with Etingof, classified symplectic resolutions (of quotient singularities and soon for quiver varieties) with Bellamy, defined new constructions of cyclic homology and its Gauss-Manin connection with Ginzburg, and I computed Hochschild (co)homology of preprojective and Frobenius algebras. In current work, I investigate connections with topological field theories, Fukaya categories, and the b-function.
From 2008--2013, I was a five-year fellow of the American Institute of Mathematics.
From 2009--2012 and 2014--2017, I received NSF standard grants.
Bitoun T, Schedler TJ, On D-modules related to the b-function and Hamiltonian flow, Compositio Mathematica, ISSN:0010-437X
Bellamy G, Schedler T, 2018, Filtrations on Springer fiber cohomology and Kostka polynomials, Letters in Mathematical Physics, Vol:108, ISSN:0377-9017, Pages:679-698
Etingof P, Schedler T, 2018, Poisson traces, D-modules, and symplectic resolutions, Letters in Mathematical Physics, Vol:108, ISSN:0377-9017, Pages:633-678
Pym B, Schedler TJ, Holonomic Poisson manifolds and deformations of elliptic algebras, Hitchin70, Oxford University Press