Periods of Algebraic Cycles and Hodge Loci - Part 1

Explore a lecture from the third GADEPs focused conference on Noether-Lefschetz and Hodge loci, delivered by Roberto Villaflor at IMPA in Rio de Janeiro. Delve into the topic of "Periods of algebraic cycles and Hodge loci" in this first part of a two-lecture series. Gain insights into the intersection of geometry, arithmetic, and differential equations through the lens of periods - certain multiple integrals. Examine the challenges surrounding Noether-Lefschetz loci in parameter spaces of algebraic surfaces and their component codimension distribution. Investigate the use of transcendental tools from periods and Hodge theory to study these loci as local analytic varieties. Learn about Hodge loci as a generalization of Noether-Lefschetz loci and explore the implications of the Cattani-Deligne-Kaplan theorem on their algebraic nature. Engage with cutting-edge research and discussions in this field, presented as part of a broader scientific program featuring mini-courses and lectures by experts in the area.