\documentstyle[12pt]{article} \pagestyle{empty} \begin{document} \begin{center} {\bf CURRICULUM VITAE} \end{center} \vspace{6mm} \begin{center} {\bf MISHA VERBITSKY} \end{center} \vspace{10mm} \begin{description} \item[Born:] June 20, 1969, Moscow, USSR \item[Citizenship:] Russia \item[Permanent Address:] 11 Orekhovy blvd., apt. 83, Moscow, 115551, Russia \item[Current Address:] 18 Tufts st., 2-nd fl. apt., Cambridge MA 02139 \item[Telephone Number (home):] 547-61-27 \item[Education:] \mbox{} \begin{itemize} \item 1990 \hspace{2mm} B.A. \hspace{2mm} Moscow State University \item 1995 \hspace{2mm} Ph.D. \hspace{2mm} Harvard University \end{itemize} \item[Positions Held:] \mbox{} \begin{itemize} \item 1990-91 \hspace{2mm} Visiting Scholar, MIT \item 1991-95 \hspace{2mm} Graduate Student, Harvard University \end{itemize} \item[Papers:] \mbox{} \begin{itemize} \item 1988 \hspace{2mm} Verbitsky M. On the action of a Lie algebra SO(5) on the cohomology of a hyperkaehler manifold. // Func. Analysis and Appl. 24(2) p 70-71 (1990). \item 1991 \hspace{2mm} Kazhdan D., Verbitsky M., Cohomology of restricted quantized universal enveloping algebras.// Quantum Deformations of Algebras and Their Representations, vol. 7 of Isr. Math. Conf. Proc. (1993) \item 1992 \hspace{2mm} Verbitsky M., Hyperholomorphic bundles over the hyperkaehler manifolds. // Electronic preprint alg-geom 9307008 (1993), 43 pp, LaTeX (accepted by J. of Alg. Geom.) \item 1993 \hspace{2mm} Verbitsky M., Hyperkaehler and holomorphic symplectic geometry I. // Electronic preprint alg-geom 9307009 (1993) 14 pp, LaTeX// also published in: Journ. of Alg. Geom., vol. 5 no. 3 pp. 401-415 (1996). \item 1994 \hspace{2mm} Verbitsky, M., Hyperk\"ahler embeddings and holomorphic symplectic geometry II. // alg-geom electronic preprint 9403006, 14 pages, LaTeX. // also published in: GAFA vol. 5 no. 1 (1995) pp. 92-104 \item 1994 \hspace{2mm} Verbitsky M., Cohomology of compact hyperkaehler manifolds. // Electronic preprint alg-geom 9501001 (1995), 85 pp, LaTeX. \item 1995 Verbitsky M., Cohomology of compact hyperkaehler manifolds and its applications // alg-geom electronic preprint 9511009, 12 pages, LaTeX.// also published in: GAFA vol. 6 no. 4 pp. 601--612 (1996) \item 1995 Verbitsky M., Mirror Symmetry for hyperkaehler manifolds, alg-geom 9512195. \item These papers are available from Harvard Math. department World Wide Web server, \begin{verbatim} http://www.math.harvard.edu:/~verbit \end{verbatim} \end{itemize} \item[Research interests:] Algebraic geometry, differential geometry, perverse \linebreak sheaves, Mirror Symmetry, cohomological methods in contact and symplectic geometry, Yang--Mills theory. \item[Brief r\'{e}sum\'{e} of research experience:] {\ } \begin{itemize} \item 1986-88 Studied the algebraic structure of the cohomology ring $H^*(M)$ of a compact hyperkaehler manifold. Proved that a Lie group $Spin(1,4)$ acts naturally on $H^*(M)$. Tried to prove Bogomolov's theorem of decomposition for Ricci-flat manifolds (with no knowledge of Bogomolov's work). \item 1990-91 Studied Yand-Mills theory. Obtained a different proof of Mukai's results about stable bundles over a K3-surface. \item 1991-92 Generalized results of Mukai to an arbitrary compact hyperkaehler manifolds $M$. Computed obstructions to the deformation of a stable holomorphic bundle over $M$. Proved that the deformation spaces of such bundles are hyperkaehler. \item 1992-93 Worked in Quantum groups. Computed cohomology of the restricted Quantum Universal Enveloping algebra, defined by Lusztig. Extensively worked with cohomology of non-com\-mu\-ta\-tive algebras. \item 1993 Worked with holomorphic symplectic geometry. Let $M$ be a compact holomorphically symplectic manifold which is generic in it's deformation class. I proved that all closed complex subvarieties of $M$ are even-dimensional and (outside of the singular locus) holomorphically symplectic. \item 1994 In the situation above, let $H$ be a hyperkaehler structure on $M$ which is compatible with the holomorphic symplectic structure. I proved that all closed complex subvarieties are complex analytic with respect to any of the complex structures induced by $H$. \item 1994 Using the results above, I constructed a theory of coherent perverse sheaves over $M$. The ``hyperkaehler'' analogues of Weil conjectures were stated in this situation, and proved in low-dimensional case. The complete version of this theory (non-\-exis\-ting, yet) should solve most of the present problems pertaining to coherent sheaves on $M$. \item 1994 Proved structure theorems about cohomology of compact hyperkaehler manifolds. Explicitly computed the ring structure of the $H^2$-generated part. \item 1995 Tried to prove similar results for a desingularization of a compact, singular hyperkaehler manifold. Obtained the action of $SU(2)$ on its second cohomology. \item 1995 Using the structure theorem for cohomology of a compact holomorphically symplectic manifold $M$, proved Mirror Conjecture for $M$. A compact holomorphically symplectic manifold is Mirror Dual to itself. \item 1995 Worked with non-unitarian Yang-Mills instantons and the twistor spaces. Established 1-1 correspondence between a certain component $S$ of a space of rational curves on a twistor space for a compact hyperkaehler manifold and a space of non-unitarian Yang-Mills instantons on a Mukai dual hyperkaehler manifold. Proved that $S$ admits a natural pluri-subharmonic function. Conjecturally, $S$ is Stein. \end{itemize} \item[Family status:] I am married, with two children, Sima and Alesha, 4 and 3 years old. My wife, Yulya Fridman, born in 1970, B. Sc. in physics, works as a translator from French to Russian. \item[Extracurricular interests:] Surrealism, dadaism, avangarde music, writings by F. Kafka, W. S. Burroughs, Ph. K. Dick, Aleister Crowley, R. A. Wilson, Clive Barker, films by R. Polansky, Monty Python's Flying Circus, Sci-Fi, horror, free masonry, Qaballah, occult, politics. \end{description} \end{document}