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Representation theory, noncommutative geometry
My research interests include representation theory, algebraic geometry, homological algebra, and mathematical physics. I am particularly interested in various interactions between these fields. Some of my recent work is related to derived algebraic geometry, algebraic homotopy theory and their applications in representation theory and low-dimensional topology.
- MATH 2930 : Differential Equations for Engineers
- MATH 4900 : Supervised Research
- MATH 4901 : Supervised Reading
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.