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Jeudi 27 février 14:00-15:00 Aaron Fenyes (IHES)
Using flat geometry to study surface group representations

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Résumé : Adding geometric structure to a surface can help you study the
representations of its fundamental group. I’ll show you how a special
kind of flat structure, called a half-translation structure, can help
you study representations into SL(2,C). Characterizing Anosov
representations and calculating shear-bend coordinates are the main
applications I plan to cover.

Using flat geometry to study surface group representations  Version PDF
Jeudi 20 février 14:00-15:00 Radhika Gupta (University of Bristol)
Non-uniquely ergodic arational trees in the boundary of Outer space

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Lieu : IMO, salle 2L8

Résumé : The mapping class group of a surface is associated to its Teichmüller space. In turn, its boundary consists of projective measured laminations. Similarly, the group of outer automorphisms of a free group is associated to its Outer space. Now the boundary contains equivalence classes of arational trees as a subset. There exist distinct projective measured laminations that have the same underlying geodesic lamination, which is also minimal and filling. Such geodesic laminations are called `non-uniquely ergodic’. I will talk briefly about laminations on surfaces and then present a construction of non-uniquely ergodic phenomenon for arational trees. This is joint work with Mladen Bestvina and Jing Tao.

Notes de dernières minutes : L’exposé sera précédé d’un café culturel assuré à 13h par Camille Horbez.

Non-uniquely ergodic arational trees in the boundary of Outer space  Version PDF
Vendredi 13 mars 15:30-16:30 Noémie Legout (Uppsala)
Exemples de cobordismes lagrangiens plongés ne provenant pas de cobordismes lagrangiens immergés par chirurgie

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Lieu : Université de Nantes, Laboratoire de Mathématiques Jean Leray, salle Eole

Résumé : Dans cet exposé, on donne des exemples de nœuds legendriens admettant des remplissages lagrangiens de genre g avec i points d’immersion (satisfaisant certaines propriétés), mais pas de remplissage de genre g-1 avec i+1 points d’immersion. Ces exemples s’obtiennent en montrant que s’il existe un cobordisme lagrangien d’une legendrienne L vers une legendrienne L’, alors le nombre de classes d’équivalence d’augmentations de L est nécessairement inférieur ou égal au nombre de classes d’équivalence d’augmentations de L’.
Ceci est un travail en collaboration avec Orsola Capovilla-Searle, Maÿlis Limouzineau, Emmy Murphy, Yu Pan et Lisa Traynor.

Exemples de cobordismes lagrangiens plongés ne provenant pas de cobordismes lagrangiens immergés par chirurgie  Version PDF
Vendredi 13 mars 14:00-15:00 Chris Wendl (Berlin)
Some remarks on transversality and symmetry

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Lieu : Université de Nantes, Laboratoire de Mathématiques Jean Leray, salle Eole

Résumé : Everyone knows that you can’t have transversality and symmetry at the same time. One familiar example for symplectic topologists is the problem caused by multiple covers in defining holomorphic curve invariants, but the trouble arises in finite-dimensional settings as well. In this talk I will explain why, in a fairly wide variety of settings, the degree of transversality that is achievable without breaking symmetry is in fact much nicer and more useful than commonly known, and I will discuss what kinds of technical results must be proved in order to establish this in any given setting. Applications include transversality results for certain classes of multiply covered holomorphic curves, and a proof that simple holomorphic curves in Calabi-Yau 3-folds are generically super-rigid.

Some remarks on transversality and symmetry  Version PDF
Mercredi 4 mars 14:00-15:00 Ksenia Fedosova (Université de Freiburg)
Selberg zeta function twisted by representations with non-expanding cusp monodromy

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Lieu : Salle 3L8

Résumé : To a hyperbolic surface and a finite-dimensional representation of its fundamental group, we associate a Selberg zeta function. The main goal of the talk is to show that under the condition that the representations have non-expanding cusp monodromy (that in particular implies that such representations need not be unitary), the Selberg zeta function exists and admits a meromorphic extension to the whole complex plane. We will also show that outside this class of representations, the Selberg zeta function does not converge.

Selberg zeta function twisted by representations with non-expanding cusp monodromy  Version PDF
Mercredi 26 février 14:00-17:00 Nicoletta Tardini (Université de Turin)
Special Hermitian metrics on complex manifolds

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Lieu : Salle 3L8

Résumé : A very special class of complex manifolds is realized by Kähler manifolds, namely complex manifolds admitting a Hermitian metric whose fundamental form is symplectic. The existence of such a metric implies sev- eral cohomological obstructions as the validity of the ∂∂-lemma. We will discuss the relations between this property and the Bott-Chern cohomol- ogy on complex non-Kähler manifolds. Moreover, several generalizations of Kähler metrics have been introduced by imposing that the fundamental form of a Hermitian metric (or its powers) is in the kernel of a suitable differential operator. One could expect that these metrics arise as critical points of naturally defined functionals on the space of Hermitian metrics. We will investigate some of these functionals, restricted to a conformal class of normalized Hermitian metrics, discussing the geometric meaning of their critical points. These are joint works with Daniele Angella, Nicolina Istrati and Alexandra Otiman.


Special Hermitian metrics on complex manifolds  Version PDF