Symplectic topology, contact topology and interactions, Paris

Thematic trimester program at Institut Henri Poincaré, Paris (Back to main page)

It has been more than 25 years ago that the previous thematic program on symplectic topology took place at Institut Henri Poincaré. Since then, the field has undergone a spectacular transformation earning itself a central position in the mathematical landscape. It interacts strongly with other fields such as dynamical systems, low dimensional topology, homotopical algebra, and algebraic geometry.

Main events:

• April 19th to 23th: Introductory Spring School (online):
  Spring school main page
   
• April 26th to 30th, research conference
  From Hamiltonian Systems to Symplectic Topology and Beyond (online)
  This conference is organized by CIRM. Please register to the above website to participate.
   
• May 17th to 21st: research conference:
  Advances in Symplectic topology (online)
   
• The third conference has been cancelled

Weekly seminar & other activities

Zoom link:

https://us02web.zoom.us/j/86503014755?pwd=Q2tkQ2gwNXVqNU5RT3crWHo2SmJxUT09

• Friday July 16th: Symplectic online seminar

  15h15 : Helmut Hofer (IAS) : The Floer jungle: 35 years of Floer theory (Organized by the Berlin Mathematical School and the Symplectic Zoominar) https://theias.zoom.us/j/97116147750?pwd=L2Fud1Y4Z2xsT3dhU2NrV0ZXd3lUQT09

• Tuesday July 13th: Symplectic online seminar

  15h00 : Morgan Weiler (RICE University): Progress towards new examples of knot-filtered ECH Abstract: Knot-filtered embedded contact homology is an invariant of an elliptic Reeb orbit of any contact form for a given contact structure on a closed, oriented three-manifold. It was introduced in a 2016 paper of Hutchings and enables embedded contact homology (ECH) to recover the Calabi invariant of the return map of a global surface of section of the Reeb vector field. Knot-filtered ECH is an invariant of the contact structure rather than the contact form, so it would be interesting to know what features of the contact structure it records. We will explain work in progress with Jo Nelson towards computing the knot filtered ECH of the right- and left-handed trefoil knots as elliptic orbits for different contact structures on S^3.

• Friday July 9th: Symplectic online seminar

  10h45 : Kaoru Ono (Kyoto) : Orbifold Lagrangian Floer theory Abstract:  I will present a set-up for orbifold Lagrangian Floer theory,  We introduce the notion of dihedral twisted sectors for Lagrangians,  intersections of Lagrangians.  Then I explain their role in the construction of  Floer theory.  It is in collaboration with Bohui Chen and Bai-Ling Wang.

  13h45 : Georgios Dimitroglou Rizell (Uppsala): Non-squeezing of Legendrian knots into neighbourhoods of non-Legendrians and C^0 contactomorphisms Abstract: We discuss joint work with M. Sullivan where we show that a contactomorphism cannot squeeze some fixed Legendrian knot into an arbitrarily small neighbourhood of a non-Legendrian knot, under the additional constraint that the two knots become isotopic inside the neighbourhood, and that the contact manifold is tight. The techniques used are Giroux's theory of convex surfaces combined with Honda's study of solid tori with convex boundary. A corollary is that a smooth image of a Legendrian under a C^0-contactomorphism is again Legendrian (here tightness is not needed).

• Friday July 2th: Symplectic online seminar

  10h45 : Nancy Hingston (College of New Jersey) : String topology and self-intersections  Abstract: String topology studies the algebraic structure of the homology of the free loop space of a manifold. I'll describe joint work with Nathalie Wahl about string topology operations, and about what these operations compute.  We have simplified, chain-level definitions for the "loop" or "string" product and coproduct. The new definitions make possible new links between geometry and loop products. For example, If the k-fold coproduct of a homology class X on LM is nontrivial, then every representative of X contains a loop with a (k+1)-fold self-intersection.

  13h45 : Leonid Polterovich (Tel Aviv) : Symplectic cohomology and ideal valued measures Abstract: I will discuss three "big fiber theorems", the Centerpoint Theorem from ‎combinatorics, the Gromov Maximal Fiber Theorem from topology, and the Non-displaceable Fiber Theorem by Entov and myself, from a unified viewpoint provided by Gromov's ideal-valued measures. The latter theory, in the symplectic context, is combined with relative symplectic cohomology developed by Varolgunes, yielding some applications to symplectic rigidity.  Necessary preliminaries will be explained.  A work in progress with Adi Dickstein, Yaniv Ganor, and Frol Zapolsky.

  15h15 : Felix Schlenk  (Tel Aviv) : Symplectically knotted cubes (Talk shared with the Symplectic Zoominar) Abstract: While by a result of McDuff the space of symplectic embeddings of a closed 4-ball into an open 4-ball is connected,  the situation for embeddings of cubes $C^4 = D^2 \times D^2$ is very different. For instance, for the open ball $B^4$ of capacity 1, there exists an explicit decreasing sequence $c_1, c_2, \dots \to 1/3$ such that for $c < c_k$ there are at least $k$ symplectic embeddings of the closed cube $C^4(c)$ of capacity $c$ into $B^4$ that are not isotopic. Furthermore, there are infinitely many non-isotopic symplectic embeddings of $C^4(1/3)$ into $B^4$.  A similar result holds for several other targets, like the open 4-cube, the complex projective plane, the product of two equal 2-spheres,  or a monotone product of such manifolds and any closed monotone toric symplectic manifold. The proof uses exotic Lagrangian tori. This is joint work with Joé Brendel and Grisha Mikhalkin.

• Tuesday June 29th: Symplectic online seminar

  15h00 : Noémie Legout (Uppsala) : Rabinowitz Floer complex for Lagrangian cobordisms. Abstract: I will define a Floer complex associated to a pair of transverse Lagrangian cobordisms in the symplectization of a contact manifold, by a count of SFT pseudo-holomorphic discs. Then I will show that this complex is endowed with an A_\infty structure. Moreover, I will describe a continuation element in the complex associated to a cobordism L and a small transverse push-off of L.

• Friday June 25th: No seminar (on account of the conference for S. Kharlamov's 70th birthday in Nantes)

• Friday June 18th : Symplectic online seminar

• Friday June 11th : Symplectic online seminar

• Friday June 4th : Symplectic online seminar

• Friday May 28th : Symplectic online seminar

• Friday May 7th : Symplectic online seminar

• Tuesday May 4th : Graduate student day at IHP
   

Organizing committee:

Scientific committee:

Program coordinated by the Centre Emile Borel at IHP Sorbonne Université, CNRS.

also supported by: