- My papers in arxiv.org
Publications: [ A list of papers | Research overview ] (PDF).
- Past conferences.
- Quaternionic structures in algebraic geometry,
16-18 November 2007, University of Glasgow.
- Supersymmetry in complex geometry:
generalized complex structures and generalized Kahler structures on complex manifolds, 4-9 January 2009,
IPMU, University of Tokyo, Japan.
- Instantons in complex geometry,
14-18 March, 2011, Laboratory of Algebraic Geometry, HSE, Moscow.
- Geometric structures on complex manifolds, 3-7 October 2011, Laboratory of Algebraic Geometry, HSE, Moscow.
Workshop on complex geometry and foliations,
dedicated to the memory of Marco Brunella, September
17-21, 2012, Laboratory of Algebraic Geometry, HSE, Moscow.
- an old homepage (not supported since 1997)
- Laboratory of Algebraic Geometry
Talks (PDF slides)
Hodge theory on nearly Kaehler manifolds,
( Workshop on
"Special Geometries in Mathematical Physics").
Hypercomplex structures on Kaehler manifolds,
La Falda, Argentina,
Workshop on Differential Geometry).
Principal Toric Fibrations,
CRM, Universite de Montreal,
Workshop on Non-linear integral transforms:
Fourier-Mukai and Nahm.)
Quaternionic Monge-Ampere equation,
Imperial College of London.
Algebraic geometry over quaternions,
Durham University, UK.
Hypercomplex manifolds with holonomy SL(n,H),
( Second workshop on
"Special Geometries in Mathematical Physics").
Technion, Haifa, Israel.
Hyperkahler SYZ conjecture, Havana, Cuba
(First Cuban Congress on
Symmetries in Geometry and Physics).
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 mini-course 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 Monge-Ampere equation, University of Delhi
(National Meet on History of Mathematical Sciences).
- 29.08.2010 Global
Torelli theorem for hyperkahler manifolds, Oberwolfach
- 26.10.2010 Stable
bundles on CP^3 and special holonomies, CIRM, Luminy
of complex manifolds IV).
Extremal metrics in quaternionic geometry, CIRM, Luminy,
a conference "Extremal metrics: evolution equations and stability".
Generalization of Inoue surfaces by Oeljeklaus-Toma and number theory,
a conference "Non-Kaehlerian aspects of complex geometry".
- Holomorphic symplectic varieties,
Courant Institute, New York University, June 4-5, 2011, FRG Workshop.
An intrinsic volume functional on almost complex
6-manifolds and nearly Kaehler geometry,
(Oberseminar Inst. fur Algebraische Geometrie, Leibniz Universitat,
Instanton bundles on CP^3 and special holonomies
(The Seventh Congress of Romanian Mathematicians, Brasov).
Formally Kähler structure on a knot space of
structures in mathematical physics," Golden Sands, Bulgaria).
Any component of moduli of polarized hyperkahler manifolds
is dense in its deformation space,
("Moduli spaces and automorphic forms", Luminy, CIRM, France).
Morse-Novikov cohomology and
Kodaira-type embedding theorem for locally
conformally Kahler manifolds,
("Complex geometry and uniformisation",
Luminy, CIRM, France).
Twistor correspondence for hyperkaehler manifolds and the space of instantons,
Trihyperkahler reduction, Cavli IPMU, University of Tokyo, Japan,
MS Seminar: Mathematics and String Theory.
Advances in hyperkahler and holomorphic symplectic geometry
(BIRS, Canada, March 11-16, 2012).
Stable bundles on non-Kahler manifolds
with transversally Kahler foliations,
("Holomophic foliations and complex dynamics",
11-15 June 2012, Poncelet Laboratory, Moscow, Russia)
"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.
Rational curves on non-Kähler manifolds,
a conference "Komplexe Analysis", 2-8 September 2012, Oberwolfach.
"Global Torelli theorem for hyperkaehler manifolds",
"International Conference on Cycles, Calibrations and
Nonlinear Partial Differential Equations Celebrating
Blaine Lawson's 70th Birthday" (October 22-28, 2012,
Stony Brook University).
"Local structure of twistor spaces", at
"Hyper-Kahler Geometry Workshop", Simons Center for
Geometry and Physics, October 29 - November 2, 2012.
Non-hyperbolicity of hyperkähler manifolds,
Kulikov's 60-th Birthday" conference (December
3-7, 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 18-22, 2013.
Ratner's theorem and ergodic complex structures,,
KIAS, Seoul, Workshop on Deformation and Moduli in Complex Geometry,
March 25-29, 2013.
- 03.067.2013, Holography principle and Moishezon twistor spaces,
Workshop ``Moduli Spaces and their Invariants in Mathematical Physics'',
CRM, Montreal, June 3-14, 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 4-7, 2013.
- 26.03.2014, Hyperkahler manifolds are non-hyperbolic, a conference "Moduli spaces of irreducible symplectic
varieties, cubics and Enriques surfaces", Laboratoire Painleve,
Lille, March 24-28, 2014.
Hypercomplex manifolds of
quaternionic dimension 2 and HKT-structures,
workshop "Complex Geometry and Lie Groups", Torino, 16-20 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, 4-8 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. 7-11, 2014, Daejeon, Korea.
- 18.08.2014 Teichmuller spaces, ergodic theory
and global Torelli theorem, SEOUL ICM 2014,
August 13-August 22, 2014.
Kahler structure on the knot space of a G2-manifold,
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
8-12 September 2014,
Faculty of Mathematics and Computer Science,
University of Bucharest.
- 19.09.2014, Holography principle and Moishezon twistor spaces,
Quaternion-Kahler manifolds and related structures
in Riemannian and algebraic geometry,
Joint Meeting of the German Mathematical Society (DMV) and
the Polish Mathematical Society (PTM),
Poznan, 17-20 September 2014.
"Kahler threefolds without subvarieties" at
Complex Geometry, Analysis and Foliations: a conference dedicated
to the memory of M. Brunella,
ICTP, Trieste, 29.09.2014-3.10.2014.
Symplectic packing for simple Kahler manifolds,
hyperkahler manifolds and tori,
Skolkovo Institute of Science and Technology,
"Geometry, Topology and Integrability",
Skolkovo, 20-25 October 2014.
"Pseudoholomorphic curves with boundaries on holomorphic Lagrangian
"Lagrangian submanifolds and related topics",
University of Milan, 4-5 December 2014.
- 2010 (Fall): A minicourse on Kaehler geometry
(Tel-Aviv University, December 2010). Slides:
- Lecture 1: Kaehler geometry and holonomy
- Lecture 2: Calabi-Yau theorem
- Lecture 3: Bochner's vanishing and Bogomolov's decomposition for Calabi-Yau manifolds
- Lecture 4:
Supersymmetry and Kaehler identities
(Math in Moscow and HSE). An advanced undergraduate
- 2001 (Fall):
Algebraic geometry over C (an advanced undergraduate course).
- 2004 (Fall):
Algebra and geometry for first-year 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 first-year students.
- Problem sheets: [ 1 | 2 | 3 | 4 | 5 | 6 | 7 ]
- There exists
a partial translation for these courses (algebra, geometry,
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 first-year students.
- Lecture notes:
- Lecture 0, Zorn's lemma and Axiom of Choice.
- Lectures 1 and 2, metric spaces, completion, p-adic numbers.
- Lectures 3 and 4, compacts in metric spaces, Heine-Borel theorem, Hopf-Rinow 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, Seifert-van Kampen theorem, free groups, Nielsen-Schreier 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 first-year student.
The author covers metric geometry (completions, compactness,
Heine-Borel and Hopf-Rinow theorem), point-set topology
(up to Tychonoff theorem, Stone's representation theorem
for Boolean algebras, and Urysohn's metrization theorem),
some category theory is included. The set-up 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, Nielsen-Schreier theorem and
Seifert-van Kampen theorem. There ara two expositions
(of equal length) going in parallel, one purely
lecture-based, 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).
- 2010 (Spring):
Analysis on manifolds
(for second-year students).
- 2010 (Fall):
(for second-year students).
- Lecture notes:
- Problem sheets (the 2005 sets, partially redone)
[ 1 | 2 | 3 | 4 | 5 ]
- Exam problems.
- Spring 2010-Fall 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.
surfaces (an advanced graduate course).
- 2012 (Spring):
topology (first year undergraduate).
- 2012 (Fall): Gromov hyperbolic groups (advanced undergraduate).
- 2013 (Spring):
(a half-semester 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 Banach-Tarski paradox,
Chebyshev Laboratory winter school (Repino, Saint-Petersburg).
| 2 ]
- Assorted notes:
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