| Résume | The origin of Hodge theory goes back to many works on elliptic, abelian
and multiple integrals (periods). In particular, Picard and Simart's book
"Théorie des fonctions algébriques de deux variables indépendantes. Vol. I, II."
published in 1897, 1906, paved the road for modern Hodge theory.
The first half of the talk is mainly about these books, for instance, I am going to explain how Lefschetz was puzzled with the computation of Picard rank (by Picard and using periods) 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.
In the second half of the talk I will discuss periods of algebraic cycles and will give some applications in identifying some components of the Noether-Lefschetz and Hodge locus. The talk is based on my book:
A course in Hodge Theory: With Emphasis on Multiple Integrals,
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