Misha Verbitsky

Instituto Nacional de Matemática Pura e Aplicada

K3 surfaces

Slides:

• Lecture 1: Ricci-flat metrics and special holonomy (August 22).
• Lecture 2: Hopf theorem (Friday, August 25, 15:30, room 236)
• Lecture 3: topology of complex surfaces (September 5)
• Lecture 4: Teichmuller spaces (September 12)
• Lecture 5: Hodge theory (October 17)
• Lecture 6: Holomorphically symplectic and C-symplectic structures (October 24)
• Lecture 7: The local Torelli theorem: injectivity of the period map (October 31)
• Lecture 8: dd^c-lemma (November 7)
• Lecture 9: The local Torelli theorem: surjectivity of the period map (November 21)
• Lecture 10: Schouten brackets and holomorphic symplectic form (November 28)

Other materials

• Assignment 1: Connections, holonomy, Calabi-Yau manifolds (August 22)
• Assignment 2: Topology of complex surfaces (September 5)
• Assignment 3: Kahler structures on homogeneous spaces (September 12)
• Assignment 4: Differential operators and connections (September 19)
• Assignment 5: Ehresmann connections and Frobenius theorem (September 26)
• Assignment 6: Sheaves and local systems (October 11)
• Assignment 7: The Riemann-Hilbert correspondence (October 17)
• Assignment 8: Integrability of almost complex structures (October 24)
• Assignment 9: Moser's isotopy lemma (October 31)
• Assignment 10: Lie superalgebras (November 7)
• Exam

Misha Verbitsky IMPA