Complex Hyperbolicity and Representations of the Fundamental Group in Non-Compact Varieties

Explore complex hyperbolicity and representations of the fundamental group in non-compact cases through this conference talk by Benoit Cadorel from Institut Élie Cartan de Lorraine. Delve into the study of complex varieties with "big" representations of their fundamental group and their algebraic and transcendental hyperbolicity properties. Examine joint work with Y. Deng and K. Yamanoi, extending hyperbolicity results to quasi-projective varieties with semi-simple, Zariski dense, big representations. Gain insights into the archimedean aspects of the proof, which combines both archimedean and non-archimedean tools. Learn about the connections to earlier work by Campana-Claudon-Eyssidieux, Yamanoi, and Brunebarbe, while also touching upon non-archimedean constructions based on building theory and the Katzarkov-Zuo reduction.