**28 aug 2018 - 4 sep 2018**

FaMAF, Universidad Nacional de Córdoba (Argentina)

K\"ahler geometry provides analytic techniques to extend results from the algebraic to the transcendental setting. *Non-K\"ahler geometry* is then the attempt to perform a separate analysis of the complex and symplectic contributions. The very ultimate aim is a tentative classification of compact complex manifolds, by means of cohomological invariants and canonical Hermitian metrics.

*First lecture*

Cohomological invariants of complex manifolds.
- Complex and almost-complex manifolds.

- The double complex of forms on a complex manifold.

- Cohomologies of complex manifolds: sheaves and elliptic Hodge theory.

- Relation between cohomologies, and the $\partial\overline\partial$-Lemma.

*Second lecture*

Special Hermitian metrics on complex manifolds.

- Hermitian metrics on complex manifolds.

- Chern connection of Hermitian metrics.

- K\"ahler manifolds.

- Hodge theory for K\"ahler manifolds and algebraic projective manifolds.

*Third lecture*

Further topics.

- Cohomologies of solvmanifolds.

- Rational homotopy theory of compact K\"ahler manifolds.

- LCK geometry as "equivariant (homothetic) K\"ahler geometry".

**Organizers:**
Adrian Andrada.

**Courses:**

28 Aug 2018: **D. Angella:** *Curso: An invitation to complex non-Kähler geometry. I.* Aula 12, FaMAF, Universidad Nacional de Córdoba

3 Sep 2018: **D. Angella:** *Curso: An invitation to complex non-Kähler geometry. II.* Aula 12, FaMAF, Universidad Nacional de Córdoba

4 Sep 2018: **D. Angella:** *Curso: An invitation to complex non-Kähler geometry. III.* Aula 12, FaMAF, Universidad Nacional de Córdoba

**Speakers:**
Daniele Angella.