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Mini course on fundamental groups of complex algebraic varieties

2025-07-07 10:18:22

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.