Linear Shafarevich Conjecture for Quasiprojective Varieties

This lecture by Benjamin Bakker from the University of Illinois Chicago explores the linear Shafarevich conjecture for quasiprojective varieties. Discover how Bakker and his collaborators, Y. Brunebarbe and J. Tsimerman, extend the work of Eyssidieux, Katzarkov, Pantev, and Ramachandran to prove a version of the linear Shafarevich conjecture for quasiprojective varieties. Learn about Shafarevich's original question regarding whether the universal cover of a smooth projective variety is always holomorphically convex, and how non-abelian Hodge theory techniques are applied to address this problem in the non-proper case. The presentation particularly emphasizes the role of twistor geometry in the stack of local systems, showcasing recent advances in this mathematical field.