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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.
The problem of lacunas and analysis on root systems, Trans. Amer. Math. Soc. 352 (2000), 3743–3776.
Automorphisms and ideals of the Weyl algebra (with G. Wilson), Math. Ann. 318 (2000), 127–147.
Ideal classes of the Weyl algebra and noncommutative projective geometry (with G. Wilson and M. van den Bergh), Internat. Math. Res. Notices 26 (2002), 1347–1396.
Cherednik algebras and differential operators on quasi-invariants (with P. Etingof and V. Ginzburg), Duke Math. J. 118 (2003), 279–337.
Morita equivalence of Cherednik algebras (with P. Etingof and V. Ginzburg), J. reine angew. Math. 568 (2004), 81–98.
A-infinity modules and Calogero-Moser spaces (with O. Chalykh), J. reine angew. Math. 607 (2007), 69–112.
Mad subalgebras of rings of differential operators on curves (with G. Wilson), Advances in Math. 212 no. 1 (2007), 163–190.