Slides:

- Lecture 1: Holonomy (March 13).
- Lecture 2: Levi-Civita connection (March 17).
- Lecture 3: Frobenius theorem (March 20).
- Lecture 4: Riemann-Hilbert correspondence (March 24).
- Lecture 5: de Rham theorem about decomposition of holonomy (March 27).
- Lecture 6: Berger list of irreducible holonomy groups (March 31).
- Lecture 7: Hyperkahler manifolds (April 3).
- Lecture 8: Bogomolov decomposition theorem (April 7).
- Lecture 9: Clifford algebras (April 10).
- Lecture 10: Spin structures (April 14).
- Lecture 11: Dirac operator (April 17).
- Lecture 12: Bochner vanishing (April 21).
- Lecture 13: Symplectic reduction (April 24, April 27).
- Lecture 14: Geometric invariant theory (May 1)
- Lecture 15: Hyperkahler reduction (May 5)
- Lecture 16: Complex subvarieties and the proof of Newlander-Nirenberg (May 8)
- Lecture 17: Trianalytic subvarieties (May 8)
- Lecture 18: Twistor spaces and equivariant bundles (May 12, May 15)
- Lecture 19: Kobayashi-Hitchin correspondence (May 18)
- Lecture 20: Yang-Mills connections (May 22)
- Lecture 21: Hyperholomorphic bundles (May 26)
- Lecture 22: Hodge theory and supersymmetry on hyperkahler manifolds (May 29)
- Lecture 23: The period map and the BBF form (June 23)
- Lecture 24: The Fujiki formula and its applications (June 26)
- Lecture 25: Lie algebra acting on cohomology (June 30)

Assignments

- Assignment 1: Kähler structures (March 13).
- Assignment 2: Holonomy and torsion (March 20).
- Assignment 3: Riemannian holonomy (March 27).
- Assignment 4: Quaternionic Hermitian structures (April 3).
- Assignment 5: Calabi-Yau manifolds and invariants theory (April 10).
- Assignment 6: Clifford algebras (April 17).
- Assignment 7: Symplectic reduction (April 24).
- Assignment 8: Geometric invariant theory (May 1).
- Assignment 9: Moore and Dieudonne determinants (May 8).
- Assignment 10: Calibrations and Wirtenger's inequality (May 15).
- Assignment 11: Holomorphic vector bundles (May 22).
- Assignment 12: Hodge theory and supersymmetry (May 29).
- Assignment 13: Verma modules (June 5).
- Assignment 14: Hodge structures (June 12).

Miscellanea

- Class assignments results (updated)
- Exam problems
- Personal problem sets, obtained randomly with this program.
- Final results (pending)

Misha VerbitskyIMPA |