a homepage
 My papers in arxiv.org

Publications: [ A list of papers  Research overview ] (PDF).

Curriculum Vitae
 Past conferences.
 Quaternionic structures in algebraic geometry,
1618 November 2007, University of Glasgow.
 Supersymmetry in complex geometry:
generalized complex structures and generalized Kahler structures on complex manifolds, 49 January 2009,
IPMU, University of Tokyo, Japan.
 Instantons in complex geometry,
1418 March, 2011, Laboratory of Algebraic Geometry, HSE, Moscow.
 Geometric structures on complex manifolds, 37 October 2011, Laboratory of Algebraic Geometry, HSE, Moscow.

Workshop on complex geometry and foliations,
dedicated to the memory of Marco Brunella, September
1721, 2012, Laboratory of Algebraic Geometry, HSE, Moscow.
 The second workshop on complex geometry and foliations
dedicated to the memory of Marco Brunella , February 25March 1, 2013,
Laboratory of Algebraic Geometry, HSE, Moscow.
 A workshop on the Chow group of holomorphically
symplectic manifolds, May 1923, 2014, Laboratory of Algebraic Geometry, HSE, Moscow.
 Complex manifolds, dynamics and birational geometry, November 1014, 2014, Laboratory of Algebraic Geometry, HSE, Moscow.
 Algebraic structures in convex geometry,
February 1620, 2015, Laboratory of Algebraic Geometry, HSE,
Moscow.
 Workshop on rationally connected varieties,
May 1822, 2015, Laboratory of Algebraic Geometry, HSE,
Moscow.
 an old homepage (not supported since 1997)
 Laboratory of Algebraic Geometry
Talks (PDF slides)
 17.03.2006,
Hodge theory on nearly Kaehler manifolds,
Kuhlungsborn, Germany,
( Workshop on
"Special Geometries in Mathematical Physics").
 08.08.2007,
Hypercomplex structures on Kaehler manifolds,
La Falda, Argentina,
(Third
Workshop on Differential Geometry).
 28.08.2007,
Principal Toric Fibrations,
CRM, Universite de Montreal,
(
Workshop on Nonlinear integral transforms:
FourierMukai and Nahm.)
 05.11.2007,
Quaternionic MongeAmpere equation,
Imperial College of London.
 26.11.2007,
Algebraic geometry over quaternions,
Durham University, UK.
 03.04.2008,
Hypercomplex manifolds with holonomy SL(n,H),
Kuhlungsborn, Germany,
( Second workshop on
"Special Geometries in Mathematical Physics").
 05.06.2008,
Sasakian manifolds,
Technion, Haifa, Israel.
 18.12.2008,
Hyperkahler SYZ conjecture, Havana, Cuba
(First Cuban Congress on
Symmetries in Geometry and Physics).
 16.01.2009,
Topology of locally conformally Kaehler manifolds,
Tokyo Metropolitan University.
 June 2009, a conference at the University of Lille 1
"Holomorphically symplectic varieties and moduli spaces".
[ 1  2  3 ] A minicourse on "Hyperkahler SYZ conjecture
and multiplier ideal sheaves".
 November 2009, a trimester and a workshop
on Kaehler and related geometries at Nantes University.
 07.01.2010, History of MongeAmpere equation, University of Delhi
(National Meet on History of Mathematical Sciences).
 29.08.2010 Global
Torelli theorem for hyperkahler manifolds, Oberwolfach
("Komplexe
Analysis" conference).
 26.10.2010 Stable
bundles on CP^3 and special holonomies, CIRM, Luminy
(Geometry
of complex manifolds IV).
 08.02.2011
Extremal metrics in quaternionic geometry, CIRM, Luminy,
a conference "Extremal metrics: evolution equations and stability".
 21.02.2011
Generalization of Inoue surfaces by OeljeklausToma and number theory,
CIRM, Luminy,
a conference "NonKaehlerian aspects of complex geometry".
 Holomorphic symplectic varieties,
Courant Institute, New York University, June 45, 2011, FRG Workshop.
 16.06.2011,
An intrinsic volume functional on almost complex
6manifolds and nearly Kaehler geometry,
(Oberseminar Inst. fur Algebraische Geometrie, Leibniz Universitat,
Hanover).
 01.07.2011,
Instanton bundles on CP^3 and special holonomies
(The Seventh Congress of Romanian Mathematicians, Brasov).

21.09.2011,
Formally Kähler structure on a knot space of
a G2manifold,
("Geometric
structures in mathematical physics," Golden Sands, Bulgaria).

11.10.2011,
Any component of moduli of polarized hyperkahler manifolds
is dense in its deformation space,
("Moduli spaces and automorphic forms", Luminy, CIRM, France).
 21.10.2011,
MorseNovikov cohomology and
Kodairatype embedding theorem for locally
conformally Kahler manifolds,
("Complex geometry and uniformisation",
Luminy, CIRM, France).
 23.01.2012,
Twistor correspondence for hyperkaehler manifolds and the space of instantons,
and 24.01.2012,
Trihyperkahler reduction, Cavli IPMU, University of Tokyo, Japan,
MS Seminar: Mathematics and String Theory.
 16.03.2012,
Trisymplectic manifolds,
Advances in hyperkahler and holomorphic symplectic geometry
(BIRS, Canada, March 1116, 2012).

14.06.2012,
Stable bundles on nonKahler manifolds
with transversally Kahler foliations,
("Holomophic foliations and complex dynamics",
1115 June 2012, Poncelet Laboratory, Moscow, Russia)
 07.08.2012,
"Global Torelli theorem for hyperkaehler manifolds,"
August 6  August 10, Kyoto University, Japan,
7th Pacific Rim Complex Geometry Conference.
 24.08.2012, "Holomorphic connections on the space of quasilines", Geometry Seminar,
Florida International University.
 07.09.2012,
Rational curves on nonKähler manifolds,
a conference "Komplexe Analysis", 28 September 2012, Oberwolfach.
 28.10.2012,
"Global Torelli theorem for hyperkaehler manifolds",
at
"International Conference on Cycles, Calibrations and
Nonlinear Partial Differential Equations Celebrating
Blaine Lawson's 70th Birthday" (October 2228, 2012,
Stony Brook University).
 29.10.2012,
"Local structure of twistor spaces", at
"HyperKahler Geometry Workshop", Simons Center for
Geometry and Physics, October 29  November 2, 2012.

07.12.2012,
Nonhyperbolicity of hyperkähler manifolds,
at "Victor
Kulikov's 60th Birthday" conference (December
37, 2012, Steklov Institute, Moscow).
 09.03.2013, Instanton bundles on $\C P^3$ and
rational curves on twistor spaces, TIFR, Mumbai, India,
International Conference on Analytic
and algebraic geometry related to bundles, March 1822, 2013.
 27.03.2013,
Ratner's theorem and ergodic complex structures,,
KIAS, Seoul, Workshop on Deformation and Moduli in Complex Geometry,
March 2529, 2013.
 03.067.2013, Holography principle and Moishezon twistor spaces,
Workshop ``Moduli Spaces and their Invariants in Mathematical Physics'',
CRM, Montreal, June 314, 2013.
 03.10.2013, Ergodic complex structures and Kobayashi metric,
"Symplectic algebraic geometry",
30/09/2013 to 04/10/2013, Kansai Seminar House, Kyoto.
 8.11.2013, Towards the cone conjecture for hyperkahler manifolds, a talk at
Quiver Varieties Program Seminar, Simons Center, Stony Brook.
 Subtwistor metric on the moduli of hyperkahler manifolds,
International conference ``Geometry and analysis on metric structrures'',
Geometric control theory laboratory, Novosibirsk, December 47, 2013.
 26.03.2014, Hyperkahler manifolds are nonhyperbolic, a conference "Moduli spaces of irreducible symplectic
varieties, cubics and Enriques surfaces", Laboratoire Painleve,
Lille, March 2428, 2014.
 16.03.2014,
Hypercomplex manifolds of
quaternionic dimension 2 and HKTstructures,
workshop "Complex Geometry and Lie Groups", Torino, 1620 June 2014.
 05.08.2014, Holography principle and Moishezon twistor spaces, Conference on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles,
National University of Singapore, 48 Aug 2014.
 10.08.2014, Complex subvarieties in homogeneous complex manifolds,
Topology of Torus Actions and Applications to Geometry and Combinatorics
(ICM Satellite conference) Aug. 711, 2014, Daejeon, Korea.
 18.08.2014 Teichmuller spaces, ergodic theory
and global Torelli theorem, SEOUL ICM 2014,
August 13August 22, 2014.
 05.09.2014,
Kahler structure on the knot space of a G2manifold,
Simons Center for Geometry and Physics, Stony Brook,
G2 manifolds: September 2  5, 2014.
 11.09.2014, Kahler threefolds without subvarieties,
a talk at
REAL and COMPLEX DIFFERENTIAL GEOMETRY
812 September 2014,
Faculty of Mathematics and Computer Science,
University of Bucharest.
 19.09.2014, Holography principle and Moishezon twistor spaces,
QuaternionKahler manifolds and related structures
in Riemannian and algebraic geometry,
Joint Meeting of the German Mathematical Society (DMV) and
the Polish Mathematical Society (PTM),
Poznan, 1720 September 2014.
 01.10.2014,
"Kahler threefolds without subvarieties" at
Complex Geometry, Analysis and Foliations: a conference dedicated
to the memory of M. Brunella,
ICTP, Trieste, 29.09.20143.10.2014.
 21.10.2014,
Symplectic packing for simple Kahler manifolds,
hyperkahler manifolds and tori,
Skolkovo Institute of Science and Technology,
International conference
"Geometry, Topology and Integrability",
Skolkovo, 2025 October 2014.
 04.12.2014,
"Pseudoholomorphic curves with boundaries on holomorphic Lagrangian
subvarieties",
a conferemce
"Lagrangian submanifolds and related topics",
University of Milan, 45 December 2014.
 05.03.2015:
Symplectic packing and hyperkahler geometry,
Workshop on Hyperkaehler Geometry,, KIAS, Seoul
Teaching
(in English)
 2010 (Fall): A minicourse on Kaehler geometry
(TelAviv University, December 2010). Slides:
 Lecture 1: Kaehler geometry and holonomy
 Lecture 2: CalabiYau theorem
 Lecture 3: Bochner's vanishing and Bogomolov's decomposition for CalabiYau manifolds
 Lecture 4:
Supersymmetry and Kaehler identities
 2013
(Spring): Geometry
of manifolds
(Math in Moscow and HSE). An advanced undergraduate
course.
(in Russian)
 2001 (Fall):
Algebraic geometry over C (an advanced undergraduate course).
Exam problems.
 2004 (Fall):
Algebra and geometry for firstyear students
(an integrated course)
 Curriculum (early stage planning).
 Problem sheets (algebra):
[ 1  2  3  4  5  6  7  8  9  10  11  12 ]
 Problem sheets (geometry): [ 1  2 ]
For the rest of geometry course, please see
the 2008 Topology lectures and problems below.
 2005 (Spring): Measure theory for firstyear students.
 Problem sheets: [ 1  2  3  4  5  6  7 ]
 There exists
a partial translation for these courses (algebra, geometry,
measure theory),
due to Dmitry Sustretov and
Dmitry Pasechnik (with many thanks).
 Of these sheets, only the problem set 5 survives now.
The rest were redone for the Fall of 2010.
 2006 (Fall): Hodge theory and its applications (an advanced undergraduate course).
Problem sheets: [ 1  2  3  4  5 ]
 2008 (Spring):
Foundations of Kaehler geometry
(an advanced undergraduate course).
[
Lecture notes for the first lecture,  exam problems. ]
 2008 (Spring):
Topology for firstyear students.
 Lecture notes:
 Lecture 0, Zorn's lemma and Axiom of Choice.
 Lectures 1 and 2, metric spaces, completion, padic numbers.
 Lectures 3 and 4, compacts in metric spaces, HeineBorel theorem, HopfRinow theorem.
 Lecture 5, Hausdorff axioms.
 Lecture 6, products topology.
 Lectures 7 and 8 , metrization theorem and compactness.
 Lecture 9, product of compact spaces, Tychonoff's theorem and ultrafilters.
 Lecture 10, Banach spaces, Frechet spaces.
 Lectures 11 and 12, the space of continuous maps, connected and path connected spaces.
 Lectures 13 and 14, totally disconnected spaces, Boolean algebras, Stone's representation theorem.
 Lecture 15, fundamental group.
 Lecture 16, universal covering and fundamental group.
 Lectures 17 and 18, Seifertvan Kampen theorem, free groups, NielsenSchreier theorem.
 Problem sheets:
[ 1  2  3  4  5  6  7  8  9  10 ]
 Mark sheets: [ 1, 2, 3  4, 5, 6  7, 8  9, 10 ]
 Exam problems.
 A book is written, based on this lectures (PDF, 4.5 Mb, to appear in Independent
University of Moscow press). Its annotation:
A beginner's course of topology,
suitable for a firstyear student.
The author covers metric geometry (completions, compactness,
HeineBorel and HopfRinow theorem), pointset topology
(up to Tychonoff theorem, Stone's representation theorem
for Boolean algebras, and Urysohn's metrization theorem),
some category theory is included. The setup is very basic
(set theory is explained from the beginnings and up to
Axiom of Choice and its applications). The book ends with
an introduction to homotopy theory; Galois coverings,
fundamental group, NielsenSchreier theorem and
Seifertvan Kampen theorem. There ara two expositions
(of equal length) going in parallel, one purely
lecturebased, another a problem based course,
suitable for a more advanced student; in the
second part, all theorems are split into series
of problems for the student to solve.
 2009 (Spring):
Geometry of complex surfaces.
 2010 (Spring): The Ricci flow and topology (an advanced undergraduate course).
Exam problems.
 2010 (Spring):
Analysis on manifolds
(for secondyear students).
 2010 (Fall):
Measure theory
(for secondyear students).
 Lecture notes:
 Problem sheets (the 2005 sets, partially redone)
[ 1  2  3  4  5 ]
 Exam problems.
 Spring 2010Fall 2011:
Kaehler manifolds and complex algebraic geometry (a graduate course).
 2011 (Summer):
Geometric group theory: amenable groups and polynomial growth.
 Slides: [ 1  2  3  4 ]
 2011 (Fall):
Commutative algebra and algebraic geometry (basic undergraduate course).
 2011 (Fall): Mori program (an advanced graduate course). Exam problems.
 2012
(Spring): Complex
surfaces (an advanced graduate course).
 2012 (Spring):
Basic
topology (first year undergraduate).
 2012 (Fall): Gromov hyperbolic groups (advanced undergraduate).
 2013 (Spring):
Galois theory
(a halfsemester course; second year undergraduate).
 Slides: [ 1  2  3  4  5  6  7  8 ]
 Problem sets: [ 1  2  3  4  5  6  7  8 ]
 Coursework and exam problems: [ 1  2  3 ]
 2013 (Summer):
Symplectic capacity and pseudoholomorphic curves
 2013 (Fall) Differential geometry and vector bundles (advanced undergraduate)
 2013 (Fall):
Amenable groups and BanachTarski paradox,
Chebyshev Laboratory winter school (Repino, SaintPetersburg).
Slides:
[ 1
 2 ]
 2014 (Spring): Complex algebraic geometry (HSE and IUM undergraduate course)
 Assorted notes:
Hosted at imperium.lenin.ru