Journée de rentrée de l'équipe Topologie & Dynamique

Programme:

Sobhan Seyfadini 9h30
    Homeomorphisms in symplectic topology
    
    This will be a brief introduction to C^0 symplectic topology.

Nina Otter 10h00
    On the effectiveness of persistent homology

    Persistent homology (PH) is, arguably, the most widely used method in Topological Data Analysis.
    In the last decades it has been successfully applied to a variety of applications, from predicting biomolecular properties,
    to discriminating breast-cancer subtypes, classifying fingerprints, or studying the morphology of leaves.
    At the same time, the reasons behind these successes are not yet well understood.
    We believe that for PH to remain relevant, there is a need to better understand why it is so successful.
    In this talk I will discuss recent work that tries to take a first step in this direction.
    The talk is based on joint work with Renata Turkeš and Guido Montúfar,
    which can be accessed at https://papers.nips.cc/paper_files/paper/2022/hash/e637029c42aa593850eeebf46616444d-Abstract-Conference.html

 Break 10h30-10h45

Russell Avdek 10h45
    Fillability and exact Lagrangians in symplectizations

    I'll state a conjecture, guessing that important properties of a contact manifold are determined by the non-existence of submanifolds in its symplectization.
    I'll sketch a proof covering everything except the hardest case using holomorphic curves and an algebraic trick.
    This reports on work with Dimitroglou Rizell.

Yuan Yao 11h15
    Fixed points of symplectic maps

    I’ll first give a general exposition of how symplectic topologists study symplectic maps using fixed-point Floer cohomology.
    Then I will explain some of my joint work with Ziwen Zhao and Maxim Jeffs on computing algebraic operations in fixed point Floer cohomology,
    and its connection to elliptic curves in algebraic geometry.

 Lunch 11h45-13h30

 Team presentation 13h30

Amandine Escalier 14h00

Local-to-Global rigidity of p-adic lattices

    In this talk we will present a rigidity notion called “Local-to-Global rigidity”
    and discuss the cases of buildings and p-adic lattices.
    We will motivate this study, present the necessary background and connect these notions
    with their analogues from the manifolds theoretic point of view.

 Break 14h30-14h45

David Xu 14h45-15h15

  Discrete groups of isometries of the infinite-dimensional hyperbolic space.

    The hyperbolic spaces have an analog of infinite dimension which shares a lot of properties with the finite-dimensional ones.
    It is in particular a metric space whose group of isometries resembles those in finite dimension.
    However, the space and its isometry group are not locally compact, which takes us out of the usual setting for geometric group theory.
    In this context, discreteness of a subgroup can be defined in several different ways.
    I am interested in finding "discrete" subgroups of this group of isometries.

Mats Bylund 15h15-15h45
    Critical recurrence in low-dimensional dynamics
    
    I will talk about some results connected to recurrence of the critical points to themselves in the low-dimensional setting (real quadratic, rational).