Speaker: Ya Deng（CNRS, Institut Élie Cartan de Lorraine）
Time: 10:00-11:00, Dec 8, 2022
Room: C1124, Material Science Research Building
It is natural to ask whether one can characterize the hyperbolicity of algebraic varieties (e.g. positivity of their logarithmic canonical bundle) via their topology. In this talk, I will answer this question if their fundamental groups admit a linear representation. Precisely, I will give a sharp condition for the hyperbolicity of complex quasi-projective varieties via representation of fundamental groups. This fits well with the prediction of the strong Green-Griffiths-Lang conjecture. If time allows, I will briefly explain the strategy of the proof, which is based on Nevanlinna theories, and non-abelian Hodge theories in both Archimedean and non-archimedean settings.
