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Demi-journée d’équipe – 25 novembre 2025
La prochaine (demi-)journée de l’équipe TGA aura lieu le mardi 25 novembre 2025, de 14h à 18h à Sophie Germain (salle 1016). Nous aurons le plaisir d’écouter :
- Alessandro Chiodo
Sur une famille de courbes lisses C au-dessus d’une base S, on considère un fibré en droite L et on étudie le lieu des points p de S où le fibré L_p est trivial sur la courbe C_p. Quand la famille C/S est lisse, ou même nodale mais irréductible, on peut définir et calculer aisément un cycle algébrique supporté sur ce lieu à l’aide des classes de Chern via la formule de Thom-Porteous. Quand cette étude est étendue à une famille de courbes stables, on peut encore définir un cycle algébrique, mais la méthode précédente échoue. Avec David Holmes on décrit plusieurs façons de déterminer ce cycle et ses variantes.
- Cyril Demarche
- Danica Kosanović : Diffeomorphisms from dancing circles
It is still unknown whether every diffeomorphism of the 4-sphere is isotopic to the identity, i.e. whether the smooth mapping class group is trivial or not. I will explain how all candidate classes constructed recently arise from 1-parameter families of embedded circles, and often reduce to a single class. Analogues of such classes have been shown to be nontrivial in some non-simply connected 4-manifolds.
- Ángel David Ríos Ortiz
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Demi-Journée des doctorant.e.s de l’équipe TGA 2025
L’édition 2025 de la demi-journée des doctorant.e.s de l’équipe TGA aura lieu le mercredi 18 juin après-midi, sur le campus des Grands Moulins, dans la salle 1015 du bâtiment Sophie Germain.
Exposés
- (14h-14h30) Gabriel Bassan : The Nori fundamental group scheme and some of its variations
The search for good substitutes to topological invariants in modern algebraic geometry has been a main topic of research since the inception of the field. This has led to many developments such as étale cohomology and the étale fundamental group. However, these often present certain limitations in positive characteristic. With this in mind, Grothendieck conjectured the existence of a « true fundamental group » in SGA I. In 1976, Madhav Nori constructed such an object, nowdays called « The Nori Fundamental group scheme ». In this talk, I will recall the definition and construction of this fundamental group and some of its variants. I will also explain some recent problems related to this object and how it relates to my resesarch.
- (14h40-15h10) Filipp Buryak : Representation stability of spaces of string links
Homological stability is a powerful tool to study homology of a sequence of spaces. However, it is often the case that our spaces are equipped with some extra structure, which turns out to be an obstruction. For example, it might happen when homology groups of our spaces are naturally $S_n$ representations. While studying such cases, Church and Farb introduced the notion of representation stability, a kind of stability which applies to the sequences of representations. In this talk, I will sketch a framework, the theory of FI modules, that is used to study this phenomenon. I will also give examples of braid groups, configuration spaces and mapping class groups. Finally, I will discuss my work in the case of spaces of string links.
- (15h20-15h50) Marie-Camille Delarue : Stable homology of Higman-Thompson groups
Thompson’s groups are groups of piecewise linear self-homeomorphisms of an interval where the cut points are dyadic rationals. Different variations of these groups exist such as the Higman-Thompson groups. This family of groups satisfies homological stability. We compute the homology of these groups in a stable range using topological scanning methods: we build a topological model for these groups in the form of categories of 1-« cobordisms » where objects are configurations of points and morphisms are paths of configurations which are allowed to collide in certain ways.
- (16h20-16h50) Léo Dubocs : Arithmetic intersection theory and non-Archimedean analogs
Arithmetic intersection theory, developed by Gillet & Soulé, strikingly mixes algebraic objects at finite places, and analytic objects at infinite places. This asymmetry motivates the search for a non-Archimedean theory, in which algebraic objects would be replaced by p-adic analytic objects.
During this presentation, I will recall the basic constructions of classical intersection theory, and discuss with more details the arithmetic theory. Finally, I’ll present two approaches, by Bloch – Gillet – Soulé and Chambert-Loir – Ducros respectively, that tend towards a non-Archimedean version.
- (17h-17h30) José São João : Lie algebra homology and Graph complexes
Lie algebra’s appear across the mathematical landscape. Their homology can often tell us important information about the Lie algebra’s one may be interested in as well as other objects they are studied in conjunction with. However sometimes computing Lie algebra homology can be difficult. Graph complexes, first mentioned by Gelfand and Fuchs (1970) and later formalised and used by Kontsevich (1993), are a useful combinatorial tool which can be used to study and compute the homology of certain Lie algebras that appear in algebra and geometry. In this talk I will speak about the result of Gelfand and Fuchs and the theorem of Kontsevich which popularised the use of graph complexes in algebra and geometry. If there is time I will mention more recent developments as well as how this relates to my research.
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