Curriculum Vitae
Education
1997-2002 Ph.D. in Mathematics, UC Berkeley. Thesis advisor: Prof. Alan Weinstein1995-1997 M.S. (Highest Distinction), Moscow Institute of Physics and Technology, Russia
1991-1995 B.S. (Highest Distinction), Moscow Institute of Physics and Technology, Russia
Employment
2010-present: Academic Administrator, UCLA2005-2010: Assistant Adjunct Professor, UCLA
2002-2005: VIGRE Assistant Professor, UCLA
1997-2002: Graduate Student Instructor/Researcher, UC Berkeley
Research Interests
My research interests lie in the rapidly developing area of Differential Geometry called Poisson Geometry. This subject has many connections with Hamiltonian mechanics, infinite-dimensional Lie algebras and deformation quantization. The idea of deformation quantization comes from the correspondence principle, which states that a quantum-mechanical system should behave like a classical system in the large-energy limit. Mathematically, this suggests a link between non-commutative algebras (the “language” behind quantum mechanics) and Poisson manifolds (the “language” behind classical mechanics). Following this idea, Weinstein initiated a research program of studying the Poisson analogs of many notions that make sense for non-commutative algebras (such as modules, bimodules, utomorphisms, Morita equivalences and so on). My current research is a part of this program. [List of Publications]Invited Research Talks
1. Picard groups and Morita equivalence in Poisson Geometry, USC Geometry and Topology Seminar, 2004.2. Picard groups of topologically stable Poisson structures, Poisson 2004, Luxembourg.
3. Bisecting the Picard group, Symplectic Geometry seminar, UC, Berkeley, 2004.
4. On gauge and Morita equivalence of Poisson manifolds, Groupoidfest, Berkeley, 2001.
5. Towards a classification of Poisson structures on surfaces, USC/Caltech; UCLA; Berkeley, 2001.
6. A complete set of invariants for generic Poisson structures on a 2-sphere, Workshop on Quantization, deformations, and new homological and categorical methods in mathematical physics, Manchester, England, 2001.
7. Poisson cohomology of certain Poisson structures on the plane, Berkeley, 1999.
8. On the algebraic structure of differential calculus on quantum groups, XVI Workshop on Geometric Methods in Physics, Bialowieza, 1997.
Invited Expository Talks
1. The Mathematics of the Musical Scales, Occidental College; CSULA, 2005.2. The Hofer-Zehnder capacity of sympletic manifolds, (2 lectures), Summer school on Hamiltonian Mechanics and Integrable systems, Lake Arrowhead, 2004.
3. What is a groupoid? Graduate Student Outreach seminar, UCLA, 2004.
4. Gelfand-Fuchs cohomology and Characteristic Classes, École Polytechnique, Paris, 1999.