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Description
Classical works by Picard, Lefschetz, Hodge, Deligne, and others have revealed that complex algebraic varieties exhibit rich topological structures—such as the Hard Lefschetz theorem, Deligne's mixed Hodge structures, and formality. In this talk, I will discuss recent developments in the topology of complex projective varieties with "big" or "large" fundamental groups, focusing on conjectures of Chern–Hopf–Thurston and Kollár concerning the (holomorphic) Euler characteristic of such varieties. I will also discuss a conjecture by Katzarkov et. al. on deformation openness properties of these varieties. This is based on a series of joint works with Chikako Mese and Botong Wang.
