Instituto Nacional de Matemática Pura e Aplicada
Hodge theory
Announcement.
Slides:
- Lecture 1: Complex manifolds,
17.03.2025
- Lecture 2: Cauchy formula
(for home perusal)
- Lecture 3: Frobenius theorem,
19.03.2025
- Lecture 4:
Real analytic manifolds
24.03.2025
- Lecture 5:
Newlander-Nirenberg theorem
26.03.2025
- Lecture 6:
Kähler structures on homogeneous spaces,
31.03.2025
- Lecture 7:
Levi-Civita connection,
02.04.2025
- Lecture 8:
Intrinsic torsion,
07.04.2025
- Lecture 9:
Bismut connection, 09.04.2025
- Lecture 9-bis, a supplement:
Harmonic forms and cohomology (for home reading).
- Lecture 10:
Lefschetz identities and supersymmetry on Kähler
manifolds, 14.04.2025
- Lecture 11:
Sheaves and cohomology, 28.04.2025
- Lecture 12:
Torus action and Dolbeault cohomology of a torus, 30.04.2025
- Lecture 13:
Poincaré-Dolbeault-Grothendieck lemma, 05.05.2025
- Lecture 14:
Chern connection, 07.05.2025
- Lecture 15:
Hodge theory for forms with coefficients in holomorphic bundle, 12.05.2025
- Lecture 16:
Kodaira-Nakano vanishing theorem, 14.05.2025
- Lecture 16-bis, a supplement:
Generalized functions and currents (for home reading).
- Lecture 17:
Non-bounded operators on Hilbert spaces, 19.05.2025
- Lecture 18:
L2-cohomology, 21.05.2025
- Lecture 19:
Holomorphically convex manifolds, 26.05.2025
- Lecture 20:
Stein manifolds, 28.05.2025
- Lecture 21:
Vanishing of cohomology for pseudoconvex manifolds, 02.06.2025
- Lecture 22:
Singular plurisubharmonic functions, 04.06.2025
- Lecture 23:
Multiplier ideals and Nadel vanishing theorem, 09.06.2025
- Lecture 24:
Kawamata-Viehweg theorem and Kodaira embedding theorem
obtained from Nadel vanishing theorem, 11.06.2025
Home assignments
Exam