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 ategorshel@gmail.com
(with cc tocornea@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)