Time：2025/8/1, 9:30-11:30; 2025/8/2, 9:30-11:30, 14:00-16:00
Venue: E4-233
Speaker：Ya Deng, CNRS，University of Lorraine
Abstract:
These three lectures will focus on the fundamental groups of algebraic varieties and their algebro-geometric properties.
In the first lecture, I will introduce non-abelian Hodge theory in the archimedean setting, namely Simpson’s correspondence between Higgs bundles and complex local systems.
The second lecture will be devoted to non-archimedean non-abelian Hodge theory, specifically the work of Gromov–Schoen on harmonic maps into Euclidean buildings associated with $p$-adic local systems on complex algebraic varieties. I will also explain how this theory leads to the construction of certain multivalued holomorphic 1-forms.
In the third lecture, I will discuss various applications of these theories, including the proofs of the reductive Shafarevich conjecture, the linear Chern–Hopf–Thurston conjecture, and the linear Kollár conjecture, among others.
