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Representation theory, noncommutative geometry, mathematical physics
My research interests include mathematical physics, algebraic geometry and representation theory. I am particularly interested in various interactions between these fields. Some of my recent work is related to noncommutative geometry, integrable systems, differential operators on algebraic varieties, representation theory of Cherednik algebras, and the theory of invariants of finite reflection groups.
Representation homology of spaces and higher Hochschild homology (with A. C. Ramadoss and Wai-kit Yeung)
Representation homology, Lie algebra cohomology and the derived Harish-Chandra homomorphism (with G. Felder, A. Patotski, A. C. Ramadoss and T. Willwacher), J. Eur. Math. Soc. 19 (2017), 2811-2893.
Stable representation homology and Koszul duality (with A.C. Ramadoss), J. Reine Angew. Math. 715 (2016), 143–187.
Double affine Hecke algebras and generalized Jones polynomials (with P. Samuelson), Compos. Math. 152 (2016), 1333–1384.
Dixmier groups and Borel subgroups (with A. Eshmatov and F. Eshmatov), Adv. Math. 286 (2016), 387–429.
Derived representation schemes and cyclic homology (with G. Khachatryan and A. C. Ramadoss), Adv. Math. 245 (2013), 625–689.
Quasi-invariants of complex reflection groups (with O. Chalykh), Compos. Math. 147 (2011), 965–1002.
Cherednik algebras and differential operators on quasi-invariants (with P. Etingof and V. Ginzburg), Duke Math. J. 118 (2003), 279–337.
Automorphisms and ideals of the Weyl algebra (with G. Wilson), Math. Ann. 318 (2000), 127–147
The problem of lacunas and analysis on root systems, Trans. Amer. Math. Soc. 352 (2000), 3743–3776.