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{\bf CURRICULUM VITAE}
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{\bf MISHA VERBITSKY}
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\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.
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