Algebraicity of the Hodge Locus in Polarized Variations of Hodge Structure

Explore the intricacies of algebraic geometry in this conference talk by Bruno Klingler from Berlin. Delve into the concept of the Hodge locus and its algebraicity within polarized variations of Hodge structures. Examine Weil's 1979 observation connecting the Hodge conjecture to the algebraic nature of the Hodge locus, and learn about the significant proof by Cattani, Deligne, and Kaplan in 1995. Investigate the central question of when the Hodge locus is fully algebraic rather than a countable union of algebraic varieties. Gain insights into joint research conducted with Baldi and Ullmo, expanding on this fundamental topic in algebraic geometry and Hodge theory.