Fundamental Groups and Algebraic Varieties - Colloquium

Attend a mathematics colloquium exploring the fundamental group of complex algebraic varieties and its geometric implications. Discover how the fundamental group π₁(X) serves as a crucial invariant connecting topology to algebraic geometry through two key questions: determining the number of simply-connected algebraic subvarieties within X, and counting global holomorphic functions on the universal cover X̃. Examine the relationship between these questions and Shafarevich's famous conjecture, which proposes that for smooth projective varieties, the universal cover possesses sufficient global holomorphic functions to separate points up to compact ambiguity. Learn about recent collaborative research with Brunebarbe and Tsimerman that provides complete solutions to both fundamental questions when π₁(X) admits a faithful linear representation, utilizing advanced techniques from non-abelian Hodge theory to bridge topological and geometric perspectives in algebraic variety theory.