HSE and Independent University
Complex algebraic geometry and Hodge theory
Wednesdays, 17:00-21:00, Saturdays, 14:00-17:00, room 306
Announcement and literature
Slides:
- Lecture 1: Differential operators (January 24, 2018)
- Lecture 2: Elliptic operators (January 27, 2018)
- Lecture 3: Compact operators (January 31, 2018)
- Lecture 4: Sobolev's $L^2$-spaces and Rellich lemma (February 3, 2018)
- Lecture 5: Fredholm operators (February 7, 2018)
- Lecture 6: Laplace operators are Fredholm (February 10, 2018)
- Lecture 7: Weitzenböck formula (February 14, 2018)
- Lecture 8: Sobolev lemma (February 17, 2018)
- Lecture 9: Almost complex manifolds (February 21, 2018)
- Lecture 10: Newlander-Nirenberg theorem (February 24, 2018)
- Lecture 11: Kähler manifolds (February 28, 2018)
- Lecture 12: Levi-Civita connection (March 3, 2018)
- Lecture 13: Bismut connection (March 7, 2018)
- Lecture 14: Supersymmetry for Kähler manifolds, part 1 (March 14, 2018)
- Lecture 15: Supersymmetry for Kähler manifolds, part 2 (March 17, 2018)
- Lecture 16: Currents, generalized functions and Poincaré-Dolbeault-Grothendieck lemma (March 21, 2018)
- Lecture 17: The proof of Poincaré-Dolbeault-Grothendieck lemma (March 24, 2018)
- Lecture 18: Sheaf cohomology (March 31, 2018)
- Lecture 19: Chern connections (April 4, 2018)
- Lecture 20: Curvature of line bundles (April 7, 2018)
- Lecture 21: Hodge theory with coefficients in a bundle (April 11, 2018)
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Lecture 22: Kodaira-Nakano vanishing theorem (April 14, 2018)
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Lecture 23: Calabi-Yau manifolds (May 16, 2018)
Handouts
- Assignment 1: Sheaves (January 24, 2018)
- Assignment 2: Differential operators (January 31, 2018)
- Assignment 3: Banach spaces and Stone-Weierstrass theorem (February 7, 2018)
- Assignment 4: Compact operators (February 14, 2018)
- Assignment 5: Fredholm operators (February 21, 2018)
- Assignment 6: Connections (February 28, 2018)
- Assignment 7: Sobolev spaces (March 7, 2018)
- Assignment 8: Cartan's formula (March 14, 2018)
- Assignment 9: Elliptic operators (March 21, 2018)
- Assignment 10: Green operator (April 4, 2018)
- Assignment 11: Exponential map (April 11, 2018)
- Assignment 12: Kahler structures on homogeneous spaces (April 18, 2018)
- Assignment 13: foliations and fibrations (April 25, 2018)
- Assignment 14: Fubini-Study form (May 2, 2018)
Miscellanea: test problems, exam, etc.