Symplectic Zoominar (CRM-Montreal, Princeton/IAS, Tel Aviv, and Paris).    



NEW !!!  ZOOM link:  https://umontreal.zoom.us/j/94366166514?pwd=OHBWcGluUmJwMFJyd2IwS1ROZ0FJdz09   NEW !!!  (backup/alternate:  https://princeton.zoom.us/j/745635914NEW !!!
 

Date and hour:  Fridays, 9:15 - 10:45 (Montreal/Princeton hour).


Regular research talks are of 60 minutes; 30 minutes  are reserved for discussion at the end of each talk (see VARIA below).


It is intended that talks be accessible to a global community in symplectic geometry/topology and beyond (thus, they should contain an  introduction of interest to a broad audience).


Once a month we intend to have a seminar consisting of three 20 min talks (followed each by 10 min of discussion time) reserved to young researchers/recent PhD's. In case you want to talk or to nominate someone,
see VARIA 4 below.





Next talk:


May 29: Alex Oancea (Paris) Duality for Rabinowitz-Floer homology

Abstract: I will explain a duality theorem with products in Rabinowitz-Floer homology. This has a bearing on string topology and explains a number of dualities that have been observed in that setting. Joint work in progress with Kai Cieliebak and Nancy Hingston.






Future talks:

June 5:     Three 20 min research talks.

Morgan Weiler (Rice):
Infinite staircases of symplectic embeddings of ellipsoids into Hirzebruch surfaces.
Abstract: Gromov nonsqueezing tells us that symplectic embeddings are governed by more complex obstructions than volume. In particular, in 2012, McDuff-Schlenk computed the embedding capacity function of the ball, whose value at a is the size of the smallest four-dimensional ball into which the ellipsoid E(1,a) symplectically embeds. They found that it contains an “infinite staircase” of piecewise-linear sections accumulating from below to the golden ratio to the fourth power. However, infinite staircases seem to be rare for more general targets. Work of Cristofaro-Gardiner-Holm-Mandini-Pires suggests that, up to scaling, there are only finitely many rational symplectic toric manifolds whose embedding capacity functions contain infinite staircases, while Usher has found infinitely many irrational polydisks with infinite staircases. Using ECH capacities in conjunction with the methods of McDuff-Schlenk, we will explain how we have found several infinite families of Hirzebruch surfaces whose embedding capacity functions we expect to contain an infinite staircase. Many of these staircases are “descending” rather than “ascending." This is joint work with Maria Bertozzi, Tara Holm, Emily Maw, Dusa McDuff, Grace Mwakyoma, and Ana Rita Pires.

Joé Brendel (Neuchatel):
Real Lagrangian Tori in toric symplectic manifolds.
Abstract: In this talk we will be addressing the question whether a given Lagrangian torus in a toric monotone symplectic manifold can be realized as the fixed point set of an anti-symplectic involution (in which case it is called "real"). In the case of toric fibres, the answer depends on the geometry of the moment polytope of the ambient manifold. In the case of the Chekanov torus, the answer is always no. This can be proved using displacement energy and versal deformations.

Abror Pirnapasov (
Bochum): Reeb orbits that force topological entropy.
Abstract: A transverse link in a contact 3-manifold forces topological entropy if every Reeb flow possessing this link as a set of periodic orbits has positive topological entropy. We will explain how cylindrical contact homology on the complement of transverse links can be used to show that certain transverse links force topological entropy. As an application, we show that on every closed contact 3-manifold exists transverse knots that force topological entropy. We also generalize to the category of Reeb flows a beautiful result due to Denvir and Mackay, which says that if a Riemannian metric on the two-dimensional torus has a contractible closed geodesic then its geodesic flow has positive topological entropy. All this is joint works with Marcelo R.R. Alves, Umberto L. Hryniewicz and Pedro A.S. Salomão

June 12: Mark Mclean (SUNY, Stony Brook), TBA

June 19: Igor Uljarevic (Belgrade)TBA

June 26: Ailsa Keating (Cambridge), TBA

July 3: Tara Holm (Cornell)/Ana Rita Pires(Edinburgh)/Alessia Maldini (Rio),   Part of Ellipsoid day joint with Western Hemisphere Virtual Symplectic Seminar

July 10: Peter Ozsvath (Princeton), TBA

July 17: Three 20 min research talks, TBA

July 24: John Pardon (Princeton), TBA




Past talks:

May 22: Denis Auroux (Harvard),  Mirrors of curves and their Fukaya categories  (slides)

May 15: Jo Nelson (Rice),  Reflections on Cylindrical Contact Homology (slides), (video)

May 8:
Marco Mazzucchelli (ENS- Lyon), Spectral characterizations of Besse and Zoll Reeb flows (slides), (video)

May 1st: Alberto Abbondandolo (Bochum),  Zoll contact forms are local maximisers of the systolic ratio (slides)

April 24:  Lisa Traynor (Bryn Mawr)The Geography of Immersed Lagrangian Fillings of Legendrian Submanifolds  (slides),  (video)

April 17:  Nicholas Wilkins (Bristol),  Equivariant quantum operations and relations between them (slides), (video)

April 10:  Leonid Polterovich (Tel Aviv),  Geometry of Quantum Uncertainty (slides), (video)

April 3:   Daniel Cristofaro-Gardiner (IAS)The Simplicity Conjecture (slides),  (video)

March 27:  Octav Cornea (Université de Montréal),  Fragmentation pseudo-metrics and Lagrangian submanifolds (slides), (video)




Varia:


1. Please do not hesitate to ask questions: first indicate your intention (or even the question) by chat, then, when invited by the host/organizer, use your microphone and  video (if available).

3. There will be 30 min at the end of each talk reserved for discussion. The first 15 minutes (roughly) are, mainly, for questions addressed to  the speaker. After that, questions and answers may involve different participants.

3. We post links to the slides of the talks as well as links to recordings of the talks (thanks to the IAS who are recording).

4.  Starting with June 5, 2020, we intend to have once a month a seminar consisting of three 20min talks (followed each by 10min of discussion time) given by young researchers/recent PhD's. Suggestions, nominations, and volunteers  (including a title and short abstract) should be sent to Egor Shelukhin at  egorshel@gmail.com (with cc to  cornea@DMS.UMontreal.CA ).




Organizers: Octav Cornea (Montreal), Egor Shelukhin (Montreal), Dan Cristofaro-Gardiner (IAS), Daniel Álvarez-Gavela (Princeton), Helmut Hofer (IAS), Yaron Ostrover (IAS), Zhengyi Zhou (IAS), Leonid Polterovich (Tel Aviv), Claude Viterbo (Paris)