Contact information

Publications – representation theory and algebra

1. Morita equivalence of deformations of Kleinian singularities, preprint.   [arXiv]


2. The inverse Galois problem for Cherednik algebras, preprint.   [arXiv]


3. On the isomorphism problem for the rings of differential operators on smooth affine varieties, preprint.   [arXiv]


4. (With Xiaojun Chen, Alimjon Eshmatov, and Farkhod Eshmatov.) On transitive action on quiver varieties,
   International Mathematics Research Notices (IMRN), in press.   [arXiv]


5. Induced subgraphs of powers of oriented cycles,
   Linear and Multilinear Algebra, in press.   [arXiv]


6. The noncommutative Noether's problem is almost equivalent to the classical Noether's problem,
   Advances in Mathematics 396, art. #108161, 2022.   [arXiv]


7. (With Apoorva Khare.)   Covering modules by proper submodules,
   Communications in Algebra 50 no. 2, pages 498-507, 2022.   [arXiv]


8. A generalization of Veldkamp's theorem for a class of Lie algebras,
   Journal of Algebra 579, pages 64-72, 2021.   [arXiv]


9. Derived invariants of the fixed ring of enveloping algebras of semisimple Lie algebras,
   Mathematische Zeitschrift 297 no. 1-2, pages 475-481, 2021.   [arXiv]


10. Generic simplicity of quantum Hamiltonian reductions,
    Comptes Rendus Mathematique (Paris) 359, pages 739-742, 2021.   [arXiv]


11. On automorphisms of enveloping algebras,
    International Mathematics Research Notices (IMRN) 2020 issue 21, pages 8183-8196, 2020.   [arXiv]


12. The Weyl algebra as a fixed ring,
    Advances in Mathematics 345, pages 756-766, 2019.   [arXiv]


13. (Appendix to paper by Benjamin Martin, David Stewart, and Lewis Topley.) A proof of the first Kac-Weisfeiler conjecture in large characteristics,
    Representation Theory 23, pages 278-293, 2019.   [arXiv]   (also subsumes arXiv:1811.10182).


14. (With Apoorva Khare.)   A Carlitz-von Staudt type theorem for finite rings,
    Linear Algebra and its Applications 568, pages 106-126, 2019.   [arXiv]


15. On the local structure of quantizations in characteristic $p$,
    Bulletin of the London Mathematical Society 50 no. 1, pages 159-165, 2018.   [arXiv]


16. Derivations of quantizations in characteristic $p$,
    Journal of Algebra 480, pages 209-214, 2017.   [arXiv]


17. Ideals in deformation quantizations over $\mathbb{Z} / p^n \mathbb{Z}$,
    Journal of Pure and Applied Algebra 221 no. 1, pages 229-236, 2017.   [arXiv]


18. (With Apoorva Khare.)   On Category $\mathcal{O}$ over triangular Generalized Weyl Algebras,
    Journal of Algebra 449, pages 687-729, 2016.   [arXiv]


19. Hochschild cohomology of deformation quantizations over $\mathbb{Z} / p^n \mathbb{Z}$,
    Algebras and Representation Theory 19 no. 1, pages 209-214, 2016.   [arXiv]


20. An analogue of the Kac-Weisfeiler conjecture,
    Journal of Algebra 383, pages 168-177, 2013.   [arXiv]


21. On maximal primitive quotients of infinitesimal Cherednik algebras of $\mathfrak{gl}_n$,
    Journal of Algebra 355 no. 1, pages 171-175, 2012.   [arXiv]


22. On the Azumaya locus of almost commutative algebras,
    Proceedings of the American Mathematical Society 139 no. 6, pages 1955-1960, 2011.   [arXiv]


23. Completions of infinitesimal Hecke algebras of $\mathfrak{sl}_2$, preprint, 2011.   [arXiv]


24. Center of infinitesimal Cherednik algebras of $\mathfrak{gl}_n$,
    Representation Theory 14, pages 1-8, 2010.   [arXiv]   (also subsumes arXiv:0810.2001).


25. (With Apoorva Khare.)   Center and representations of infinitesimal Hecke algebras of $\mathfrak{sl}_2$,
    Communications in Algebra 38 no. 2, pages 405-439, 2010.   [arXiv]   (also subsumes arXiv:0604498).


26. Infinitesimal Hecke algebra of $\mathfrak{sl}_2$ in positive characteristic,
    Journal of Algebra 321 no. 1, pages 117-127, 2009.   [arXiv]


27. The center and representations of infinitesimal Hecke algebras,
    PhD Thesis, University of Chicago, 2007.


28. Homological constructions on N-complexes,
    Journal of Pure and Applied Algebra 176 no. 2-3, pages 213-222, 2002.


29. Cross-effects of Mackey functors,
    Communications in Algebra 30 no. 9, pages 4211-4218, 2002.


30. Remarks on the Vasconcelos conjecture,
    Bulletin of the Georgian National Academy of Sciences 162 no. 2, pages 213-215, 2000.


31. Subdivision of the simplicial and semisimplicial objects,
    Bulletin of the Georgian National Academy of Sciences 159 no. 3, pages 396-398, 1999.

Publications – complex analysis

1. On the Dirichlet problem in the plane with polynomial data, preprint.   [arXiv]


2. On the corona problem for strongly pseudoconvex domains, preprint.   [arXiv]


3. On regularity of the Berezin transform on smooth pseudoconvex domains, preprint.   [arXiv]


4. (With Trieu Le.)   A generalization of the Brown-Halmos theorems for the unit ball,
   Advances in Mathematics, in press.   [arXiv]


5. (With Sonmez Sahutoglu.)   On a theorem of Bishop and commutants of Toeplitz operators in $\mathbb{C}^n$,
   Rend. Circ. Mat. Palermo 68 no. 2, pages 237-246, 2019.   [arXiv]


6. Invertibility of Toeplitz operators with polyanalytic symbols,
   Advances in Operator Theory 4 no. 4, pages 793-801, 2019.   [arXiv]


7. (With Trieu Le.)   Commutants of Toeplitz operators with harmonic symbols,
   New York Journal of Mathematics 23, pages 1723-1731, 2017.   [arXiv]


8. Commutants of Toeplitz operators with monomial symbols,
   Complex Analysis and Operator Theory 11 no. 4, pages 943-946, 2017.   [arXiv]


9. Multiplication operators on the Bergman spaces of pseudoconvex domains,
   New York Journal of Mathematics 21, pages 1327-1345, 2015.   [arXiv]


10. Centralizers of Toeplitz operators with polynomial symbols,
    Complex Analysis and Operator Theory 6 no. 6, pages 1275-1279, 2012.   [arXiv]