Research

Research Interests: Algebraic geometry and Representation theory.

My current research deals with Langlands Duality, KZB connection, chiral algebras, and connections with irregular singularities.

I am also interested in mirror symmetry, Frobenius manifolds, quantum groups, and Quantum Field Theory.

You can download my entire CV here.

Work in progress

• Chiral algebras and the Casimir connection

Preprints

• An example of Langlands correspondence for irregular rank two connections on P¹ (joint with D. Arinkin). arXiv:1003.6112, submitted.

Publications

• Frobenius manifold structures on the spaces of abelian integrals. Journal of Geometry and Physics, Vol. 61 (2011), no. 2, pp. 485-497. DOI 10.1016/j.geomphys.2010.10.015. A preprint is available at arXiv:math/0701581.
• Irregular Wakimoto modules and the Casimir connection. Selecta Mathematica (N.S.), Vol. 16 (2010), no. 2, pp. 241-266. DOI 10.1007/s00029-010-0019-x. A preprint is available at arXiv:0812.4472.
• Algebraic and hamiltonian approaches to isostokes deformations, Transformation Groups, Vol. 11 (2006), no. 2, pp. 137-160. A preprint is available at arXiv:math/0412121.
• Upper bounds of the number of orbital topological types of planar polynomial vector fields "modulo limit cycles", Proceedings of the Steklov Institute of Mathematics, Vol. 254, pp. 238-254. A preprint is available at arXiv:math/0402214. Russian original: Верхние оценки числа орбитальных топологических типов полиномиальных векторных полей на плоскости "по модулю предельных циклов", Труды Математеского института им. В.А. Стеклова, 2006, Том 254, стр. 254-271.
• Upper bounds of the number of orbital topological types of polynomial vector fields on the plane "modulo limit cycles" Russian Mathematical Surveys, 2004, Vol. 59, No. 3, pp. 569-570. Russian original: Верхние оценки числа орбитальных топологических типов полиномиальных векторных полей на плоскости "по модулю предельных циклов", Успехи Мат. Наук, 2004, Том 59, Номер 3, стр. 183-184.
• Lower bounds for the number of orbital topological types of planar polynomial vector fields "modulo limit cycles", Moscow Math. J., 2001, Vol. 1, No. 4. pp. 539--550.

Recent Talks

• March 2009: MIT, Noncommutative Algebra Seminar, Non-highest weight representations of affine Kac-Moody algebras, DMT connection, and irregular Wakimoto modules.
• March 2009: Boston University, Geometry seminar, Irregular Wakimoto modules and DMT connection.
• February 2009: University of North Carolina at Chapel Hill, Physically Inspired Mathematics, Non-highest weight representations of Kac-Moody algebras and D-modules on Cartan subalgebras.
• January 2008. Boston University, Boston University Geometry Seminar, Langlands Transform and Painleve Equations.
• November 2007. The University of Pennsylvania, Math-Physics Joint Seminar, Deformations of algebro-geometric solutions of Kadomtsev-Petviashvili equations and Frobenius manifolds.
• April 2007. North Eastern University, "Isomonodromic deformations and affine Lie groups", talk at the Geometry-Algebra-Singularities-Combinatorics Seminar.
• February 2007. Massachusetts Institute of Technology, "Frobenius manifold structures on the spaces of abelian integrals", talk at the Infinite-Dimensional Algebra Seminar.
• February 2007. University of Massachusetts, Amherst, "Frobenius manifold structures on the spaces of abelian integrals", talk at the Valley Geometry Seminar.
• May 2006. California University of Technology, "Moduli spaces, Frobenius manifolds, and Whitham equations", talk at the Algebraic Geometry seminar.
• February 2006. University of Massachusetts, Series of talks on Renormalization at the Quantum Field Theory seminar.

Seminars

• Boston University Geometry Seminar
• Geometric Langlands Program
• Riemann Surfaces, Lie algebras, and Mathematical Physics