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Séminaire Symplectique

organisé par l'équipe Géométrie

  • Eduardo Fernández

    Symplectic zoominar: Cabling families of Legendrian embeddings

    19 janvier 2024 - 15:15Salle de séminaires IRMA

    Abstract: I will discuss a recursive formula for the homotopy type of the space of Legendrian embeddings of sufficiently positive cables with the maximal Thurston-Bennequin invariant. Via this formula, we identify infinitely many new components within the space of Legendrian embeddings in the standard contact 3-sphere that satisfy an injective h-principle. These components include those containing positive Legendrian torus knots with the maximal Thurston-Bennequin invariant. This work is a collaboration with Hyunki Min.

  • Yuhan Sun

    Séminaire Symplectix, sur zoom : Cech complex of the symplectic cohomology

    2 février 2024 - 15:45A confirmer

    Le séminaire sera projeté en salle C41


    Symplectic cohomology behaves like a presheaf under the Viterbo restriction map. For a Liouville domain, if it is covered by Poisson-commuting Liouville subdomains then we will show the symplectic cohomology forms a sheaf on this cover. This enables us to do local-global computations via its Cech complex. Explicit examples will be discussed in the setting of Lagrangian torus fibrations, and of the Cieliebak-Oancea exact sequence for cobordisms. Joint with U. Varolgunes.

  • Alberto Abbondandolo

    Symplectic Zoominar: Symplectic capacities of domains close to the ball and Banach-Mazur geodesics in the space of contact forms

    16 février 2024 - 15:15Salle de séminaires IRMA

    An old open question in symplectic topology is whether all normalized capacities coincide on convex bounded domains in the standard symplectic vector space. I will discuss this question for domains which are close to the Euclidean ball and its connection with the geometry of the space of contact forms with a Banach-Mazur pseudo-metric. This talk is based on a recent joint work with Gabriele Benedetti and Oliver Edtmair.

  • Denis Auroux

    Symplectic Zoominar: Floer-theoretic corrections to the geometry of moduli spaces of Lagrangian tori

    23 février 2024 - 15:15Salle de séminaires IRMA

    Given a Lagrangian torus fibration on the complement of an anticanonical divisor in a Kahler manifold, one usually constructs a mirror space by gluing local charts (moduli spaces of objects of the Fukaya category supported on generic torus fibers) via wall-crossing transformations determined by counts of Maslov index 0 holomorphic discs; this mirror also comes equipped with a regular function (the superpotential) which enumerates Maslov index 2 holomorphic discs. Holomorphic discs of negative Maslov index deform this picture by introducing inconsistencies in the wall-crossing transformations; the geometric features of the corrected moduli space of objects of the Fukaya category can be understood in the language of extended deformations of Landau-Ginzburg models. We will illustrate this phenomenon on an explicit example (a 4-fold obtained by blowing up a toric variety), and, if time permits, discuss a family Floer approach to the geometry of the corrected mirror in this setting.

  • Pierre Berger

    Séminaire symplectix (à distance) : An AbC principle for pseudo-rotations

    1 mars 2024 - 15:45Salle de séminaires IRMA

    We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive, with respectively only 2 and 1 periodic points. This solves problems of proposed by Herman (1998), Fayad-Katok (2004) and Fayad-Krikorian (2018). To establish these results, we introduce a principle that enables to realize, by an analytic symplectomorphism, properties which are C⁰-realizable by the approximation by the conjugacy method of Anosov-Katok.

  • Robert Lipshitz

    Symplectic Zoominar: Strongly invertible knots, Khovanov homotopy, and localization

    8 mars 2024 - 15:15Salle de séminaires IRMA

    Strong inversions are a class of order-2 symmetries of knots in S^3. Building on work of Seidel-Smith, Lidman-Manolescu, Stoffregen-Zhang, and others, we will describe a relationship between the Khovanov homology of a knot with a strong inversion and its quotients by the inversion. We will also give a modest application to surfaces in 4-space. This is joint work with Sucharit Sarkar. While there is no symplectic geometry in the talk, many of the ideas come from or may be useful in Floer-theoretic settings.

  • Yusuke Kawamoto

    Symplectic zoominar: Quantitative Floer theory and coefficients

    15 mars 2024 - 14:15Salle de séminaires IRMA

    I will discuss how much the choice of coefficients impacts the quantitative information of Floer theory, especially spectral invariants. In particular, I will present some phenomena that are specific to integer coefficients, including an answer to a variant of a question posed by Nancy Hingston. The material is based on a joint work with Egor Shelukhin.

  • Salammbo Connolly

    Séminaire Symplectix (à distance) : On torsion in (bi)linearized Legendrian contact homology

    5 avril 2024 - 15:45Salle de séminaires IRMA

    Given a Legendrian submanifold in a contact manifold, one can define its Legendrian Contact Homology (LCH). This invariant is unfortunately difficult to compute. However, there exist two more computable variants, linearized LCH (defined by Chekanov), and bi-linearized LCH (defined by Bourgeois and Chantraine). For legendrian knots in R^3, very little is known about the possibility of having torsion in these invariants when they are defined over integer coefficients. In joint work with Frédéric Bourgeois, we give properties of torsion that can appear in linearized LCH with integer coefficients, and also give the full geography of bi-linearized LCH with integer coefficients.

  • Laurent Côté

    Séminaire Symplectix (à distance) : Morse-Bott methods in Floer homotopy theory

    26 avril 2024 - 10:45Salle de séminaires IRMA

    I will talk about a joint project with Y. Baris Kartal whose purpose is to incorporate Morse--Bott methods into Floer homotopy theory. Morse--Bott methods have the prospect of being useful for two reasons. First, they simplify equivariant constructions: for example, we used these methods to define a lift of circle equivariant symplectic homology to equivariant spectra. Second, they enable new computations. As a step in this direction, we used Morse--Bott methods to compute the (equivariant) local Floer homology of the orbit of an autonomous Hamiltonian, but I hope and expect that one can push such computations significantly further.