Murphy's Law in non-abelian Hodge theory

par Gregorio Baldi (Paris Sud (ALGaNT))

mercredi 18 nov. 2026, 14:00 → 15:00 Europe/Paris

In this joint work with J. Lam, we discuss explicit examples of non-integral variations of Q-Hodge structures. Our approach leverages Fenchel--Nielsen-type parameterizations, due to Kabaya and Maskit, of the Teichmüller component of relative character varieties. Additionally, we discuss various Diophantine results concerning the O_{K,S}-integral points of such character varieties, and give a new proof of Beauville's classical theorem on families of elliptic curves. If time permits, pathological behaviors of the Hodge locus of non-integral QVHS will also be presented.