Claire Voisin | Hodge structures and the topology of algebraic varieties

Throughout the 20-21 academic year, the CMSA will be hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars. Talks will take place throughout the semester. All talks will take place virtually.

Written articles will accompany each lecture in this series and be available as part of the publication “The Literature and History of Mathematical Science“

Speaker: Claire Voisin (Collège de France)

Title: Hodge structures and the topology of algebraic varieties

Abstract: We review the major progress made since the 50's in our understanding of the topology of complex algebraic varieties. Most of the results we will discuss rely on Hodge theory, which has some analytic aspects giving the Hodge and Lefschetz decompositions, and the Hodge-Riemann relations. We will see that a crucial ingredient, the existence of a polarization, is missing in the general Kaehler context.
We will also discuss some results and problems related to algebraic cycles and motives.