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Attend a specialized mathematics conference exploring the intersection of algebraic geometry, arithmetic, and differential equations through the lens of periods and Hodge theory. Delve into the complex mathematical structures of Noether-Lefschetz and Hodge loci, which represent fundamental objects in algebraic geometry that arise in parameter spaces of algebraic surfaces. Examine how periods - certain multiple integrals - provide transcendental tools for studying these loci as local analytic varieties, and explore the challenging problems regarding the distribution and codimension of their components.
Engage with cutting-edge research through four comprehensive mini-courses delivered by leading experts: Roberto Villaflor presenting foundational concepts across two lectures, Gregorio Baldi exploring theoretical frameworks in two sessions, Patrick Brosnan examining advanced applications through two presentations, and François Greer discussing recent developments in two lectures. Participate in eight additional research talks where specialists present their latest findings and methodologies in related fields.
Discover how the deep theorem of Cattani, Deligne and Kaplan establishes that Hodge loci, while initially appearing as analytic varieties, are actually branches of algebraic varieties, though questions about their field of definition remain open. Learn about the generalization from classical Noether-Lefschetz theory to the broader framework of Hodge loci, and understand how these mathematical objects connect geometry, arithmetic, and differential equations.
Access discussions on the latest developments in this rapidly evolving field, including computational approaches, theoretical advances, and open problems that continue to challenge researchers. Benefit from the collaborative environment designed to foster communication between experts working on different aspects of periods, Hodge theory, and algebraic geometry, providing insights into both established results and emerging research directions in this sophisticated area of pure mathematics.
