Séminaire Géométrie et applications
organisé par l'équipe Géométrie
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Yusuke Kawamoto
Diviseur de Donaldson et l'homologie de Floer quantitative.
6 janvier 2025 - 14:00Salle de séminaires IRMA
Nous allons voir dans cet exposé une comparaison des informations quantitatives des homologies de Floer d'une variété symplectique et un diviseur de Donaldson. -
Tullio Ceccherini-Silberstein
Notions de soficité pour les groupes et les monoïdes et applications
6 janvier 2025 - 15:30Salle de séminaires IRMA
La notion de soficité pour les groupes a été introduite par M. Gromov (1999) et indépendamment par B. Weiss (2000) comme une généralisation commune de la finitude résiduelle et de la moyennabilité. Cette notion s’est révélée très efficace puisque les groupes sofiques satisfont deux fameuses conjectures (encore ouvertes en toute généralité), celle de Gottschalk dans le cadre des systèmes dynamiques symboliques (théorème de Gromov-Weiss) et celle de Kaplansky sur la stabilité finie des anneaux de groupes (théorème d'Elek-Szabo). En collaboration avec Michel Coornaert (2014) et puis aussi avec Xuan Kien Phung (2024), on a étendu la notion de soficité aux monoïdes. Dans ce laïus, je voudrais présenter ces notions de soficité (pour les groupes et les monoïdes) avec des exemples et des caractérisations, ainsi que les généralisations des théorèmes de Gromov-Weiss et Elek-Szabo au cas monoïdale. -
Gianluca Faraco
Absolute and relative period realization of abelian differentials on Riemann surfaces
13 janvier 2025 - 15:30Salle de séminaires IRMA
A translation surface is the datum of an abelian differential on a Riemann surface. Every such a pair determines a representation called absolute period character. In this talk we discuss the realization of a given representation as the period character of some translation surface. This based on joint works with D. Chen. -
Seungook Yu
Contact Instantons and Legendrian Floer Cohomology in One-Jet Bundles
3 février 2025 - 15:30Salle de séminaires IRMA
In the study of Floer theory in contact geometry, symplectization has been widely used. However, the symplectization process may result in the loss of geometric or topological information inherent to the given contact manifold. To address this, it is necessary to develop Floer theory directly on contact manifolds without relying on symplectization. Contact instantons have been introduced as a tool to achieve this goal. In this talk, I will introduce the notion of contact instanton and its analytic properties, and then use them to define Legendrian Floer cohomology for Legendrian submanifolds that are Hamiltonian isotopic to the zero section in one-jet bundles. If time permits, I will also discuss the construction of spectral invariants as an application. This is based on a joint work with Yong-Geun Oh. -
Shah Faisal
Extremal Lagrangian tori in toric domains
10 février 2025 - 15:30Salle de séminaires IRMA
I will explain Cieliebak-Mohnke's conjectures about extremal Lagrangian tori and our progress so far. If time permits, I will also discuss some applications to symplectic embedding problems. -
Vincent Dumoncel
A quasi-isometric classification of permutational wreath products
10 mars 2025 - 15:30Salle de séminaires IRMA
It is in general a hard problem to determine whether two given finitely generated groups are quasi-isometric, even among some "well behaved" classes. One such class, which has been the subject of intensive research in group theory, is the one of wreath products, as they often exhibit unexpected and interesting behaviours. The classification up to quasi-isometry of lamplighters over Z goes back to 2013, and in a recent work (2021), Genevois and Tessera extended it to all lamplighters over finitely presented one-ended groups. This raises the question of also classifying their permutational variants. In this context, strong rigidity phenomenon as the ones observed for standard wreath products do not hold, whence the need of another approach. After having introduced and discussed several re-inforcements of quasi-isometries, I will sketch the main guidelines of the proof of a quasi-isometric classification of some permutational wreath products, that covers a number of classical cases. If time permits, we will also discuss some applications and open problems. -
Elia Fioravanti
Automorphisms of virtually special groups
17 mars 2025 - 14:00Salle de séminaires IRMA
Mapping class groups, Out(F_n) and GL_n(Z) are three important groups in geometric group theory that arise as outer automorphism groups of other groups (respectively, of surface, free and free abelian groups). In general, it can be rather complicated to describe the structure of the group Out(G) for more general groups G, particularly if only certain properties of G are known. I will outline some of the work of Rips and Sela in the 90s, which completely describes Out(G) for any Gromov-hyperbolic group G, based on a canonical JSJ decomposition of G. Then I will talk about a new canonical JSJ decomposition for the compact special groups of Haglund and Wise, and how this can be used to gain information on Out(G) for any virtually special group G. -
Chikako Mese
Harmonic Maps into Euclidean Buildings
17 mars 2025 - 15:30Salle de séminaires IRMA
We establish a regularity result for equivariant harmonic maps from the universal cover of a Riemannian manifold into a Euclidean building, without assuming local finiteness. As an application, we prove a non-Archimedean superrigidity theorem for rank-1 symmetric spaces, extending the work of Gromov and Schoen, who proved p-adic superrigidity under the assumption of locally finite targets. This work is joint with C. Breiner and B. Dees. -
Mélanie Bertelson
Sur certains aspects quantitatifs en géométrie conformément symplectique
24 mars 2025 - 15:30Salle de séminaires IRMA
Les structures localement conformément symplectiques apparaissent naturellement en géométrie de contact et présentent des aspects quantitatifs intéressants et nouveaux. Certains de ces aspects seront décrits durant l'exposé. -
Blandine Galiay
Convexes divisibles dans les variétés de drapeaux
31 mars 2025 - 14:00Salle de séminaires IRMA
Un convexe divisible est un ouvert propre de l'espace projectif qui admet une action cocompacte d'un sous-groupe discret du groupe projectif linéaire. L'exemple le plus connu est l'espace hyperbolique plongé dans l'espace projectif via le modèle de Klein, mais il existe également des exemples qui ne sont pas des espaces symétriques Riemanniens. L'étude de ces objets s'appelle la théorie des convexes divisibles, et est développée depuis les années 60. Une généralisation au cas où l'espace ambiant n'est plus l'espace projectif mais une variété de drapeaux quelconque G/P a été initiée par A. Zimmer. Une question de Limbeek-Zimmer est alors : existe-t-il des exemples d'ensembles convexes divisibles dans G/P qui ne sont pas symétriques ? Dans un certain nombre de cas, il a été prouvé que ce n'était pas le cas; on dit alors qu'il y a rigidité. Dans cet exposé, nous exposerons des résultats allant dans le sens de cette rigidité, avec une attention particulière pour les grassmanniennes. -
Gabriele Viaggi
Effective length-projection bounds for hyperbolic 3-manifolds diffeomorphic to S x R
31 mars 2025 - 15:30Salle de séminaires IRMA
Hyperbolic 3-manifolds diffeomorphic to S x R where S is a closed orientable surface of genus at least 2 are well-studied objects that admit a rich deformation theory. By the solution of the Ending Lamination Conjecture, they are parametrized by a pair of end invariants, each of which is a combination of minimal filling lamination and finite area hyperbolic metric on proper essential subsurfaces of S. By this description it should be possible to turn the end invariants into concrete geometric control on the hyperbolic metric. Groundbreaking work of Minsky and Brock, Canary, and Minsky provides such a dictionary. In particular, they show that if the end invariants have a so-called large subsurface projection to a subsurface Y of S then the geodesic representative of the boundary of Y in the 3-manifold is short, and they even provide a coarse formula for its length. However, their bounds rely on various compactness arguments which make the constant involved not computable. In this talk, following a different path, I will describe an effective (computable) formula for the length of the boundary of Y in terms of subsurface projection. -
Samuel Bronstein
A slice of Anosov representations in SL(3,R)
22 avril 2025 - 11:00Salle de conférences IRMA
We study a specific class of representations of a closed surface group, parametrized via the Non Abelian Hodge correspondence by holomorphic half cubic differentials. Using the structure of the Higgs bundle, we construct domains of discontinuity in the flag variety and show that these representations are Anosov. This is joint work with Colin Davalo.