BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Ana Rechtman (Université de Strasbourg): Broken books and Reeb dy
namics in dimension 3
DTSTART;VALUE=DATE-TIME:20210518T130000Z
DTEND;VALUE=DATE-TIME:20210518T135000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5350@indico.math.cnrs.fr
DESCRIPTION:Giroux’s correspondance gives\, in particular\, for every co
ntact structure on a closed 3-manifold an adapted open book decomposition.
Hence\, it exists a Reeb vector that is tangent to the binding and transv
erse to the interior of the pages. For this vector field\, each page is a
Birkhoff section and the dynamics of the flow can be studied from the firs
t return map. This correspondence is unsatisfactory when one wants to stud
y all the Reeb vector fields associated to a contact structure. \n\nIn col
laboration with V. Colin and P. Dehornoy\, we proved that every non-degene
rate Reeb vector field on a closed 3-manifold is adapted to a broken book
(a generalisation of an open book). This construction gives a system of tr
ansverse surfaces with boundary and allows to establish results on the dyn
amics of the vector field.\n\nhttps://indico.math.cnrs.fr/event/5787/contr
ibutions/5350/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5350/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Cristofaro-Gardiner (IAS and UC Santa Cruz): The Kapovich-Polt
erovich question
DTSTART;VALUE=DATE-TIME:20210518T143000Z
DTEND;VALUE=DATE-TIME:20210518T152000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5351@indico.math.cnrs.fr
DESCRIPTION:The group of Hamiltonian diffeomorphisms of a symplectic manif
old admits a remarkable bi-invariant metric\, called Hofer’s metric. Ma
ny basic questions about the geometry of this metric remain open. For exa
mple\, in 2006 Kapovich and Polterovich asked whether or not this group\,
in the case of the two-sphere\, is quasi-isometric to the real line. I wi
ll explain joint work with Humilière and Seyfaddini resolving this questi
on: we show that the group contains quasi-isometric copies of R^n for any
n\, and we also show that the group is not coarsely proper. Key to our pr
oofs is a new sequence of spectral invariants defined via Hutchings’ Per
iodic Floer Homology.\n\nhttps://indico.math.cnrs.fr/event/5787/contributi
ons/5351/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5351/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Urs Frauenfelder (Universität Augsburg): Frozen planet orbits.
DTSTART;VALUE=DATE-TIME:20210519T143000Z
DTEND;VALUE=DATE-TIME:20210519T152000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5353@indico.math.cnrs.fr
DESCRIPTION:Frozen planet orbits are periodic orbits in the Helium atom\,
which play an important role in the semiclassical treatment of Helium. In
the talk I discuss them from a mathematical point of view and explain how
they are related to Hamiltonian delay equations.\n\nhttps://indico.math.cn
rs.fr/event/5787/contributions/5353/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5353/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Buhovsky (Tel Aviv University): On Fabry's quotient theorem.
DTSTART;VALUE=DATE-TIME:20210520T143000Z
DTEND;VALUE=DATE-TIME:20210520T152000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5355@indico.math.cnrs.fr
DESCRIPTION:The Fabry quotient theorem states that for a complex power ser
ies with unit radius of convergence\, if the quotient of its consecutive c
oefficients tends to s\, then the point z=s is a singular point of the ser
ies. In my talk I will try to describe an elementary proof of the theorem.
\n\nhttps://indico.math.cnrs.fr/event/5787/contributions/5355/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5355/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Traynor (Bryn Mawr College): Legendrian Torus and Cable Links
.
DTSTART;VALUE=DATE-TIME:20210521T143000Z
DTEND;VALUE=DATE-TIME:20210521T152000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5357@indico.math.cnrs.fr
DESCRIPTION:Legendrian torus knots were classified by Etnyre and Honda. I
will explain the classification of Legendrian torus links. In particular\,
I will describe restrictions on the Legendrian torus knots that can be re
alized as the components of a Legendrian torus link\, and I will give exam
ples of Legendrian torus links that cannot be destabilized even though the
y do not have maximal Thurston-Bennequin invariant. Furthermore\, I will e
xplain that there are some smooth symmetries of Legendrian torus links tha
t cannot be realized by a Legendrian isotopy. These torus link statements
have extensions to Legendrian cable links. All these results are applicati
ons of convex surface theory. This is joint work with Jennifer L. Dalton a
nd John B. Etnyre.\n\nhttps://indico.math.cnrs.fr/event/5787/contributions
/5357/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5357/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Russel Avdek (Uppsala Universitet): Holomorphic curve invariants o
f convex hypersurfaces.
DTSTART;VALUE=DATE-TIME:20210521T130000Z
DTEND;VALUE=DATE-TIME:20210521T135000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5356@indico.math.cnrs.fr
DESCRIPTION:Let S be a convex hypersurface with neighborhood N(S) inside o
f some contact manifold. When dim(S)=2 the contact topology of N(S) is gov
erned by simple closed curves on S. However\, few tools are currently avai
lable to study N(S) when dim(S)>2. We provide such a tool which is applica
ble in any dimension by computing the sutured contact homology of N(S) in
terms of linearized invariants of the positive and negative regions of S.
The proof combines Morse-Bott\, obstruction bundle gluing\, and virtual pe
rturbation techniques.\n\nhttps://indico.math.cnrs.fr/event/5787/contribut
ions/5356/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5356/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Hryniewicz (RWTH-Aachen): Reeb flows in dimension three wi
th exactly two periodic orbits
DTSTART;VALUE=DATE-TIME:20210517T130000Z
DTEND;VALUE=DATE-TIME:20210517T135000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5346@indico.math.cnrs.fr
DESCRIPTION:In this talk I will present a complete characterization of Ree
b flows on closed 3-manifolds with precisely two periodic orbits. The main
step consists in showing that a contact form with exactly two periodic Re
eb orbits is non-degenerate. The proof combines the ECH volume formula wit
h a study of the behavior of the ECH index under non-degenerate perturbati
ons of the contact form. As a consequence\, the ambient contact 3-manifold
is a standard lens space\, the contact form is dynamically convex\, the R
eeb flow admits a rational disk-like global surface of section and the dyn
amics are described by a pseudorotation of the 2-disk. Moreover\, the peri
ods and rotation numbers of the closed orbits satisfy the same relations a
s (quotients of) irrational ellipsoids\, and in the case of S^3 the transv
erse knot-type of the periodic orbits is determined. Joint work with Crist
ofaro-Gardiner\, Hutchings and Liu.\n\nhttps://indico.math.cnrs.fr/event/5
787/contributions/5346/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5346/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro del Pino Gómez (Universiteit Utrecht): Flexibility of dis
tributions through convex integration.
DTSTART;VALUE=DATE-TIME:20210519T130000Z
DTEND;VALUE=DATE-TIME:20210519T135000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5352@indico.math.cnrs.fr
DESCRIPTION:Building on the work of Nash on C1-isometric embeddings\, Grom
ov devised a method\, called convex integration\, to construct and classif
y solutions of partial differential relations. For the scheme to work\, on
e must assume that the relation in question is ample (and often open as we
ll). The idea behind ampleness is that it allows us to start with a formal
solution and add to it rapidly oscillating perturbations\, one direction
at a time\, in order to produce an actual solution that is C0-close.\nOne
of the issues of convex integration is that it is notoriously difficult to
apply as a blackbox. It has been applied successfully to many relations o
f geometric origin\, but always assuming (as far as the speaker knows) tha
t "the relation is ample in all directions" (or at least that shortness ho
lds in all directions). This condition means that\, regardless of the form
al data we start with\, adding suitable oscillations along an arbitrary (!
) frame of directions will allow us to produce a solution.\nIn this talk I
will discuss an example of differential relation where "ampleness in all
directions" fails but convex integration still applies. The relation under
study characterises a concrete family of non-degenerate distributions of
rank 4 in dimension 6 (which therefore satisfy the h-principle). This is j
oint work with F.J. Martínez Aguinaga.\n\nhttps://indico.math.cnrs.fr/eve
nt/5787/contributions/5352/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5352/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Bowden (Universität Regensburg): Open books\, Bourgeois
contact structures and their properties
DTSTART;VALUE=DATE-TIME:20210520T130000Z
DTEND;VALUE=DATE-TIME:20210520T135000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5354@indico.math.cnrs.fr
DESCRIPTION:Twenty years ago Frederic Bourgeois introduced a construction
of contact structures on the product of any contact manifold M with a 2-to
rus given a choice of compatible open book\, whose existence was proven by
Giroux-Mohsen. In particular\, this yielded contact structures on all odd
-dimensional tori answering a question of Lutz from the 70’s. A systemat
ic study of these contact manifolds was initiated by Lisi-Marinkovic-Niede
rkrüger and Gironella\, the former asking several questions\, which we ad
dress in this talk.\nIn particular\, we show that if the initial contact m
anifold is 3-dimensional the resulting contact structure is tight\, indepe
ndent of the initial contact structure and choice of open book. Furthermor
e\, we show that given ANY contact manifold one can always stabilise the o
pen book so that the resulting contact structure is not strongly symplecti
cally fillable. This then yields (many) examples of weakly but not strongl
y fillable contact structures in all dimensions. (joint work with F. Giron
ella and A. Moreno)\n\nhttps://indico.math.cnrs.fr/event/5787/contribution
s/5354/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5354/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jo Nelson (Rice University): Embedded Contact Homology of Prequan
tization Bundles
DTSTART;VALUE=DATE-TIME:20210517T143000Z
DTEND;VALUE=DATE-TIME:20210517T152000Z
DTSTAMP;VALUE=DATE-TIME:20221127T145400Z
UID:indico-contribution-5347@indico.math.cnrs.fr
DESCRIPTION:In 2011\, Farris provided a means of computing Z_2-graded embe
dded contact homology (ECH) of prequantization bundles over Riemann surfac
es\, producing an isomorphism between ECH of the bundle and the exterior a
lgebra of the homology of the base. In joint work with Morgan Weiler\, we
upgrade to a full Z-grading on the chain complex and obtain a stabilizati
on result. We additionally explain how to make the Morse-Bott computatio
ns rigorous by means of the direct limits for filtered ECH established in
Hutchings-Taubes proof of the Arnold-Chord conjecture. We comment on futu
re work on knot filtered ECH of certain Seifert fiber spaces.\n\nhttps://i
ndico.math.cnrs.fr/event/5787/contributions/5347/
LOCATION:ZOOM (En ligne)
URL:https://indico.math.cnrs.fr/event/5787/contributions/5347/
END:VEVENT
END:VCALENDAR