Lunedì 17 Marzo 2025, dalle ore 14:00 in Aula 2109 (2° Piano) - Edificio U5, Arnaud Maret (Università di Strasburgo) e Matteo Penegini (Università degli Studi di Genova) terranno i seguenti seminari
Relatore: Arnaud Maret
Titolo: Finite mapping class group orbits on character varieties
Abstract: A natural group to associate to an surface is its mapping class group which is the group of isotopy classes of diffeomorphisms of the surface. The mapping class group acts on the space of conjugacy classes of morphisms from the fundamental group of the surface into some Lie group - a so-called character variety. In this talk we'll investigate the rare phenomenon of finite orbits for mapping class group dynamics on character varieties. We'll see how to construct non-trivial examples of finite orbits and give some intuition on how to classify all finite orbits when the target Lie group is SL(2,C). Most of this work is a collaboration with Samuel Bronstein.
Relatore: Matteo Penegini
Titolo: Arithmetic Zariski multiplets of irreducible plane curves
Abstract: Multicanonically embedded surfaces in projective space give rise to irreducible branch curves via projection from generic axes. Building on our previous work, we transfer results from the moduli space of surfaces to strata of plane curves. For instance, the faithful action of the Galois group on the connected components of the moduli spaces of surfaces isogenous to a product, as established by Bauer, Catanese, and Grunewald, gives rise to many arithmetic Zariski multiplets. This is a joint project with M. Loenne.
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