Part 1. (march-may)
Lecture 1. (Friday March 03, 2017, 09:00-11:00, Aula Tricerri.) Analytic functions of several complex variables. [Voi1, Chapter 1]
Lecture 2. (Thursday March 09, 2017, 17:00-19:00, Aula 7.) Categories; Abelian categories. [Voi1, Chapter 4]
Lecture 3. (Thursday March 16, 2017, 17:00-19:00, Aula 7) Derived functors; presheaves and sheaves. [Voi1, Chapter 4]
Lecture 4. (Thursday March 23, 2017, 17:00-19:00, Aula 7.) Cohomology of sheaves. [Voi1, Chapter 4]
Lecture 5. (Monday April 03, 2017, 08:30-10:30, Aula Tricerri.) G-structures, almost-complex structures, differential geometry of complex manifolds. [Voi1, Chapter 2], [BHPV, Chapter VI]
Lecture 6. (Tuesday April 11, 2017, 08:30-10:30, Aula CDM-214.) Examples of complex manifolds; Fr\"olicher spectral sequence. [Voi1, Chapter 8]
Lecture 7. (Thursday April 20, 2017, 09:00-11:00, Aula CDM-227.) Leray-Serre spectral sequence; Riemannian and Hermitian manifolds. [Voi1, Chapter 5]
Lecture 8. (Thursday May 11, 2017, 09:00-11:00, Aula Tricerri.) Elliptic Hodge theory for Riemannian and Hermitian manifolds. [Voi1, Chapter 5], [Ara, Chapter 8], [BDIP, Chapter I.3]
Lecture 9. (Friday May 19, 2017, 09:00-12:00, Aula 1.) Hodge theory for compact Kaehler manifolds. [Voi1, Chapters 3-6]
Lecture 10. (Thursday May 25, 2017, 09:00-12:00, Aula 1.) Hodge conjecture. [Voi1, Chapter 7, Chapter 11], [Lew, Chapters 5-6-7]
Part 2. (october-november)
Lecture 11. Yau's estimates for non-homogeneous Monge-Ampère equations, I.
Lecture 12. Yau's estimates for non-homogeneous Monge-Ampère equations, II.
Lecture 13. Yau's estimates for non-homogeneous Monge-Ampère equations, III.
Lecture 14. Yau's estimates for non-homogeneous Monge-Ampère equations, IIII.
Seminars.
Francesco Pediconi, "Deformazioni di strutture complesse". (Tuesday September 12, 2017, xx:00-xx:00, Aula X).
Pietro Gheri, "TBA". (XX XXXX XX, 2017, xx:00-xx:00, Aula X).
Luca Sodomaco, "TBA". (XX XXXX XX, 2017, xx:00-xx:00, Aula X).
Possible seminars.
Hodge theory of compact complex surfaces and Lamari criterion. [BHPV, Chapter IV]
Elliptic Hodge theory. [BDIP, Chapter I.3], [Voi1, Chapter 5]
Relative Hodge theory, and deformations of complex structures. [Voi1, Chapters 9-10]
Vuletescu and Voisin counterexamples to Hodge conjecture for non-projective Kaehler manifolds. [Lew]
Serre's Algebraic Geometry and Analytic Geometry. [Ara, Chapters 15-16]
Kodaira embedding and balanced metric. [Voi, Chapter 7]
...
References.