Why Markman's Theorem Saves the Hodge Conjecture from Kontsevich's Tropical Counterexamples - Part 1

Explore a conference talk from the third GADEPs (Geometry, Arithmetic and Differential Equations of Periods) focused conference on Noether-Lefschetz and Hodge loci. Delve into Patrick Brosnan's lecture titled "Why Markman's theorem saves the Hodge conjecture (for Weil type abelian fourfolds) from Kontsevich's tropical counterexamples - Part 1". Gain insights into the intersection of geometry, arithmetic, and differential equations through the lens of periods and their applications to challenging problems in algebraic surfaces. Discover how transcendental tools from Hodge theory are used to study Noether-Lefschetz loci and their generalization to Hodge loci. Learn about recent developments in this field, including the implications of Cattani, Deligne, and Kaplan's theorem on the algebraic nature of Hodge loci. Engage with cutting-edge research presented by experts in the field, and understand the significance of this topic in modern mathematics.