mini-course on Hodge theory

20 Juin

mini-course on Hodge theory

Hossein Movasati (scientific expert CIMI)will give a series of Lectures

Title: Five lectures in Hodge Theory

The origin of Hodge theory goes back to many works on elliptic, abelian
and multiple integrals. In this lecture series I am going to explain how Lefschetz
was puzzled with the computation of Picard rank and this led him to consider
the homology classes of curves inside surfaces. This was ultimately formulated
in Lefschetz (1,1) theorem and then the Hodge conjecture which is one of the
millennium problems of Clay Mathematical Institute. The Hodge theory of
hypersurfaces and in particular Fermat varieties is emphasized.

The lectures are based on the books which are available in my webpage.

H. Movasati, A Course in Hodge Theory: With Emphasis on Multiple Integrals,  Somerville, MA: International Press Boston, 2021.
H. Movasati, R. Villaflor, A Course in Hodge Theory: Periods of Algebraic cycles,  33 Colóquio Brasileiro de Matemática, IMPA, Rio de Janeiro, Brazil,2021.

Lecture 1:
14 June  Room E. Picard (1R2-129) 10:30.
Title: Lefschetz  puzzle and Picard’s formula

Lecture 2:
16 June  Room E. Picard (1R2-129) 13:30
Title:  Lefschetz theorems on the topology of smooth projective varieties and Picard-Lefschetz theory

Lecture 3:
30 June  Room J. Cavailles (1R2-132) 13:30.
Title: Toward a computational proof of Lefschetz (1,1) theorem.

Lecture 4:
05 July  Room E. Picard (1R2-129) 13:30.
Title: Griffiths theorem on the cohomology of hypersurfaces.

Lecture 5:
07 July  Room E. Picard (1R2-129) 13:30
Title: Hodge cycles  for the Fermat variety.