Misha Verbitsky

a homepage

• My papers in arxiv.org
• Publications: [ A list of papers | Research overview ] (PDF).
• Curriculum Vitae
• 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.
• 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 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.
  
  • [ 1 | 2 | 3 ] A mini-course on Sasakian and locally conformally Kaehler geometry.
  • 13.11.2009, Global Torelli theorem for hyperkaehler manifolds
• 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.
  
  • Global Torelli theorem for hyperkaehler manifolds (June 4).
  • Subtwistor metric on the moduli of hyperkaehler manifolds and its applications (June 5).
• 16.06.2011, Inst. fur Algebraische Geometrie, Leibniz Universitat, Hanover, Oberseminar,
  An intrinsic volume functional on almost complex 6-manifolds and nearly Kaehler geometry.

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

(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).
• 2009 (Spring): Geometry of complex surfaces.
  • A course's summary.
  • Lecture notes:
    • Lecture 1: Kodaira-Enriques classification.
    • Lecture 2: positive currents and Hahn-Banach theorem.
    • Lecture 3: Elliptic operators, Gauduchon metric and strong maximum principle.
    • Lecture 4: Surfaces with even b₁ and Gauduchon metrics.
    • Lectures 5 and 6: Montel spaces, Kaehler currents and the theorem of Lamari.
    • Lecture 7: The Kobayashi-Hitchin correspondence and Bogomolov's theorem on surfaces of class VII.
  • Exam problems.
• 2010 (Spring): The Ricci flow and topology (an advanced undergraduate course). Exam problems.
• 2010 (Spring): Analysis on manifolds (for second-year students).
  • Problem sheets: [ 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 ]
  • English translation for the first two, by Sasha Anan'in: [ 1 | 2 ]
  • Mark sheets: [ 1-3 | 4-6 | 7-9 ]
  • Exam problems.
• 2010 (Fall): Measure theory (for second-year students).
  • Lecture notes:
    • Lecture 1: Triangulation of polyhedral bodies.
    • Lectures 2-3: Measure theory for polyhedra. Dehn's invariant.
    • Lecture 4: Boolean algebras and measurable sets
    • Lecture 5: Measurable functions.
    • Lecture 6: Hahn's decomposition, Radon-Nikodym's and Fubini's theorems.
    • Lecture 7: Caratheodory's extension theorem.
    • Lecture 8: Haar measure.
  • 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).
  • Slides: [ 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 ]
  • Problem sets: [ 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 11 | 12 | 13 | 14 | 15 | 16 | 17 ]
  • Exam problems: [ 1 | 2 ]
• Assorted notes:
  • C0-estimates in Calabi-Yau theorem (2006)
  • C2-estimates in Calabi-Yau theorem (2008)
  • An integrated math curriculum (written in 2002 for students of mathematics at ITEP).

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