Hyperbolicity in Presence of a Large Local System

Explore the intriguing world of hyperbolicity in complex algebraic geometry through this conference talk by Yohan Brunebarbe from Université de Bordeaux. Delve into the influential conjectures proposed by Green-Griffiths and Lang, which connect various notions of hyperbolicity for projective complex algebraic varieties. Discover how the locus swept out by entire curves relates to the locus swept out by subvarieties not of general type. Learn about the validity of these conjectures for varieties admitting a large complex local system, including those with variations of mixed Hodge structures and finite period maps. Gain insights into the fascinating interplay between hyperbolicity, algebraic geometry, and complex analysis in this 55-minute presentation from the "Periods, Shafarevich Maps and Applications" conference held at the University of Miami.