HSE and Independent University
Complex algebraic geometry and Hodge theory
Wednesdays, 17:0021:00, Saturdays, 14:0017:00, 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: NewlanderNirenberg theorem (February 24, 2018)
 Lecture 11: Kähler manifolds (February 28, 2018)
 Lecture 12: LeviCivita 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 PoincaréDolbeaultGrothendieck lemma (March 21, 2018)
 Lecture 17: The proof of PoincaréDolbeaultGrothendieck 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)

Lecture 22: KodairaNakano vanishing theorem (April 14, 2018)

Lecture 23: CalabiYau manifolds (May 16, 2018)
Handouts
 Assignment 1: Sheaves (January 24, 2018)
 Assignment 2: Differential operators (January 31, 2018)
 Assignment 3: Banach spaces and StoneWeierstrass 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: FubiniStudy form (May 2, 2018)
Miscellanea: test problems, exam, etc.