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Let G be a compact Lie group and let M = G/H be a G-homogeneous space, equipped with an invariant metric. We prove that the spectral norm of any compact exact Lagrangian submanifold of the cotangent bundle T*M is bounded in terms of the diameter and dimension of G. Our proof is by sheaf theoretical methods; it recovers some results of Shelukhin and gives some other cases. This is a joint work in progress with Nicolas Vichery.

53DXX ; 70Hxx ; 54B40

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Symplectic embedding problems are at the heart of the study of symplectic topology, and are closely related with Hamiltonian dynamics. In this talk we discuss how to compute the symplectic inner and outer radii of certain convex domains using the theory of integrable systems.
The talk is based on a joint work with Vinicius Ramos.

53DXX

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In the late 70s, Fathi showed that the group of compactly supported volume-preserving homeomorphisms of the ball is simple in dimensions greater than 2. We present our recent article which proves that the remaining group, that is area-preserving homeomorphisms of the disc, is not simple. This settles what is known as the simplicity conjecture in the affirmative. This is joint work with Dan Cristofaro-Gardiner and Vincent Humiliere.

53DXX ; 53D40 ; 37E30

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Unlike other similar groups, these groups remained very poorly understood for a long time. I'll review some recent progress in two directions: (non)-simplicity and the existence of quasimorphisms. I'll also give some ideas on the proofs which are based on tools from symplectic topology. This is based on joint works with Dan Cristofaro-Gardiner, Cheuk-Yu Mak, Sobhan Seyfaddini, and Ivan Smith.

53D40 ; 37J06

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This partly expository talk focuses on the notion of ”symplectic Landau-Ginzburg models”, i.e. symplectic manifolds equipped with maps to the complex plane, ”stops”, or both, as they naturally arise in the context of mirror symmetry. We describe several viewpoints on these spaces and their Fukaya categories, their monodromy, and the functors relating them to other flavors of Fukaya categories. (This touches on work of Abouzaid, Seidel, Ganatra, Hanlon, Sylvan, Jeffs, and others).[-]

This partly expository talk focuses on the notion of ”symplectic Landau-Ginzburg models”, i.e. symplectic manifolds equipped with maps to the complex plane, ”stops”, or both, as they naturally arise in the context of mirror symmetry. We describe several viewpoints on these spaces and their Fukaya categories, their monodromy, and the functors relating them to other flavors of Fukaya categories. (This touches on work of Abouzaid, Seidel, Ganatra, ...[+]

53D37 ; 14J33 ; 53D40

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For a given symplectic manifold and a finite set of Lagrangian submanifolds which intersect transversally each other we can construct an $A_{\infty }$-category. When we consider Lagrangian submanifolds which are not necessary intersect transversally there are issues to perform such a construction. In this talk I want to explain a way to study this situation. It can be used to compose Lagrangian correspondences without assuming transversality.

53D40 ; 18G99 ; 57R99

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The spectral norm is an important invariant of a Hamiltonian diffeomorphism and its properties have recently found numerous nontrivial applications to dynamics. We will explore the behavior of the spectral norm under iterations of a Hamiltonian diffeomorphism and some related phenomena. This feature is closely related to the existence of invariant sets (the Le Calvez–Yoccoz type theorems), Hamiltonian pseudo-rotations, rigidity and the strong closing lemma. The talk is based on joint work with Erman Çineli and Viktor Ginzburg.[-]

The spectral norm is an important invariant of a Hamiltonian diffeomorphism and its properties have recently found numerous nontrivial applications to dynamics. We will explore the behavior of the spectral norm under iterations of a Hamiltonian diffeomorphism and some related phenomena. This feature is closely related to the existence of invariant sets (the Le Calvez–Yoccoz type theorems), Hamiltonian pseudo-rotations, rigidity and the strong ...[+]

53D40 ; 37J11 ; 37J46

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The aims of this talk are two-fold: a) to give a biased overview of some structural properties of (smooth) symplectic mapping class groups, together with some key proof ingredients, and b) to present some open questions, both about those groups and about their $C^{0}$ counterparts, whose study was recently initiated by Alexandre Jannaud.

53D05 ; 53D40 ; 57R17

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An old open question in symplectic dynamics asks whether all normalized symplectic capacities coincide on convex domains. I will discuss this question and show that the answer is positive if we restrict the attention to domains which are close enough to a ball. The proof is based on a “quasi-invariant” normal form in Reeb dynamics, which has also implications about geodesics in the space of contact forms equipped with a Banach-Mazur pseudo-metric. This talk is based on a joined work with Gabriele Benedetti and Oliver Edtmair.[-]

An old open question in symplectic dynamics asks whether all normalized symplectic capacities coincide on convex domains. I will discuss this question and show that the answer is positive if we restrict the attention to domains which are close enough to a ball. The proof is based on a “quasi-invariant” normal form in Reeb dynamics, which has also implications about geodesics in the space of contact forms equipped with a Banach-Mazur pse...[+]

37J11 ; 53D35 ; 57R40

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I discuss some results and conjectures on contact aspects of non-equilibrium thermodynamics. Joint with Michael Entov, Shin-itiro Goto, Shai Lerer, and Lenya Ryzhik.

82Cxx ; 53DXX ; 37Jxx

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Documents Humilière, Vincent 11 résultats

On the Viterbo conjecture about Lagrangian spectral norms - Guillermou, Stéphane (Auteur de la Conférence) | CIRM H Nouveau

On symplectic radii of $\ell_p$-products - Ostrover, Yaron (Auteur de la Conférence) | CIRM H Nouveau

On the algebraic structure of groups of area-preserving homeomorphisms - Seyfaddini, Sobhan (Auteur de la Conférence) | CIRM H Nouveau

Recent progress on groups of area-preserving homeomorphisms - Humilière, Vincent (Auteur de la Conférence) | CIRM H Nouveau

Symplectic Landau-Ginzburg models and their Fukaya categories - Auroux, Denis (Auteur de la Conférence) | CIRM H Nouveau

Inductive limit which appears in Lagrangian Floer theory - Fukaya, Kenji (Auteur de la Conférence) | CIRM H Nouveau

The spectral norm, rigidity and all that - Gurel, Basak (Auteur de la Conférence) | CIRM H Nouveau

Symplectic mapping class groups: structural properties from smooth to $C^{0}$ - Keating, Ailsa (Auteur de la Conférence) | CIRM H Nouveau

Symplectic capacities of domains close to the ball and quasi-invariant contact forms - Abbondandolo, Alberto (Auteur de la Conférence) | CIRM H Nouveau

Contact topology and thermodynamics - Polterovich, Leonid (Auteur de la Conférence) | CIRM H Nouveau