a homepage
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 Non-linear integral transforms:
Fourier-Mukai and Nahm.)
- 05.11.2007,
Quaternionic Monge-Ampere 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 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
("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 Oeljeklaus-Toma and number theory,
CIRM, Luminy,
a conference "Non-Kaehlerian aspects of complex geometry".
- Holomorphic symplectic varieties,
Courant Institute, New York University, June 4-5, 2011, FRG Workshop.
- 16.06.2011,
An intrinsic volume functional on almost complex
6-manifolds 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 G2-manifold,
("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,
Morse-Novikov cohomology and
Kodaira-type 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 11-16, 2012).
-
14.06.2012,
Stable bundles on non-Kahler manifolds
with transversally Kahler foliations,
("Holomophic foliations and complex dynamics",
11-15 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 non-Kähler manifolds,
a conference "Komplexe Analysis", 2-8 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 22-28, 2012,
Stony Brook University).
- 29.10.2012,
"Local structure of twistor spaces", at
"Hyper-Kahler Geometry Workshop", Simons Center for
Geometry and Physics, October 29 - November 2, 2012.
-
07.12.2012,
Non-hyperbolicity of hyperkähler manifolds,
at "Victor
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.
- 27.03.2013,
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.
- 16.03.2014,
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.
- 05.09.2014,
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.
- 01.10.2014,
"Kahler threefolds without subvarieties" at
Complex Geometry, Analysis and Foliations: a conference dedicated
to the memory of M. Brunella,
ICTP, Trieste, 29.09.2014-3.10.2014.
- 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, 20-25 October 2014.
- 04.12.2014,
"Pseudoholomorphic curves with boundaries on holomorphic Lagrangian
subvarieties",
a conferemce
"Lagrangian submanifolds and related topics",
University of Milan, 4-5 December 2014.
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.
Teaching
(in English)
- 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
- 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 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,
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 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).
Exam problems.
- 2010 (Spring):
Analysis on manifolds
(for second-year students).
- 2010 (Fall):
Measure theory
(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.
- 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 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).
Slides:
[ 1
| 2 ]
- Assorted notes:
Hosted at imperium.lenin.ru