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, quiver varieties, and Hamiltonian reductions) with Bellamy and Craw; studied deformations of Poisson manifolds with Brent Pym, defining a new nondegeneracy condition called "holonomicity" (motivated by D-modules); 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 algebraic differential operators, birational geometry, matrix factorisations and Tate-Hochschild cohomology, and other topics.
From 2008--2013, I was a five-year fellow of the American Institute of Mathematics, and I received NSF standard grants.
Bellamy G, Schedler T, 2020, Symplectic resolutions of quiver varieties, Selecta Mathematica, ISSN:1022-1824
Negron C, Schedler T, 2020, The Hochschild cohomology ring of a global quotient orbifold, Advances in Mathematics, Vol:364, ISSN:0001-8708, Pages:1-49
Bellamy G, Schedler T, 2019, On symplectic resolutions and factoriality of Hamiltonian reductions, Mathematische Annalen, Vol:375, ISSN:0025-5831, Pages:165-176
Bitoun T, Schedler TJ, 2018, On D-modules related to the b-function and Hamiltonian flow, Compositio Mathematica, Vol:154, ISSN:0010-437X, Pages:2426-2440