Workshop on Symplectic Geometry, Contact Geometry and

Transcription

Workshop on Symplectic Geometry, Contact Geometry and Interactions
VI Workshop on Symplectic Geometry, Contact Geometry and Interactions
Madrid, February 2-4, 2012
Index Venue Speakers Registration Funding Organizers Programme Practical information Participants
Basic information:
Latest updates
Webpage created, September 2011
This is the sixth meeting on Symplectic Geometry, Contact Geometry and Interactions..Previous editions of the workshop have taken place
Registration now open, October 2011
in Lille, Brussels, Strasbourg, Paris and Uppsala.
List of lodging grants communicated in Dec 6
2011 Uppsala http://www2.math.uu.se/inform/symplec/
2010 Paris http://www.math.polytechnique.fr/~viterbo/Workshop2010.html
2009 Strasbourg http://www-irma.u-strasbg.fr/annexes/conferences/symplec/
List of participants updated as of 19 Dec
2008 Brussels http://homepages.ulb.ac.be/~symplec/
2007 Lille http://math.univ-lille1.fr/~symplec/
Programme is now complete, January 4. You
can download it here.
The conference will start on Thursday February 2 at 3pm and will finish on Saturday 4 before lunch. This year the conference joins
forces with the GESTA group. GESTA 2012 has been fusioned with this workshop.
Venue
The meeting will take place at ICMAT (aula AZUL)
C/ Nicolás Cabrera, 13-15
Campus Cantoblanco, UAM
28049 Madrid
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/[14/7/16 20:38:06]
ICMAT: The orange room on the left, outside view on the right
Documents in pdf: Programme of the conference and instructions of
arrival:
Download here the programme
NEW! Download here the "survival kit" (instructions of arrival).
Contact
For any queries concerning practical aspects of the conference please contact eithre
Fran Presas or .Eva Miranda Template design by Six Shooter Media.
Basic information:
Latest updates
Webpage created, September 2011
This is the sixth meeting on Symplectic Geometry, Contact Geometry and Interactions..Previous editions of the workshop have taken place
Registration now open, October 2011
in Lille, Brussels, Strasbourg, Paris and Uppsala.
List of lodging grants communicated in Dec 6
2011 Uppsala http://www2.math.uu.se/inform/symplec/
2010 Paris http://www.math.polytechnique.fr/~viterbo/Workshop2010.html
2009 Strasbourg http://www-irma.u-strasbg.fr/annexes/conferences/symplec/
List of participants updated as of 19 Dec
2008 Brussels http://homepages.ulb.ac.be/~symplec/
2007 Lille http://math.univ-lille1.fr/~symplec/
Programme is now complete, January 4. You
can download it here.
The conference will start on Thursday February 2 at 3pm and will finish on Saturday 4 before lunch. This year the conference joins
forces with the GESTA group. GESTA 2012 has been fusioned with this workshop.
Venue
The meeting will take place at ICMAT (aula AZUL)
28049 Madrid
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/index.html[14/7/16 20:38:08]
ICMAT: The orange room on the left, outside view on the right
Documents in pdf: Programme of the conference and instructions of
arrival:
Download here the programme
NEW! Download here the "survival kit" (instructions of arrival).
Contact
For any queries concerning practical aspects of the conference please contact eithre
Fran Presas or .Eva Miranda Template design by Six Shooter Media.
Speakers
List of speakers:
Florent Balacheff (Lille)
Rémi Cretois (Lyon)
Jacqueline Espina (Lyon)
Jonathan Evans (Zurich)
Hélène Eynard-Bontemps (Paris)
Penka Georgieva
(Princeton)
Clément Hyvrier
(Uppsala)
Yael Karshon (Toronto)
Samuel Lisi (Brussels)
Ignasi Mundet i Riera
(Barcelona)
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/speakers.htm[14/7/16 20:38:12]
Speakers
Las
Meninas by Diego Velázquez
You can see the original at Prado museum during your visit to Madrid
Template design by Six Shooter Media.
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/speakers.htm[14/7/16 20:38:12]
Registration
Registration:
This conference has no registration fee. Coffe breaks and lunch of Friday are included for all participants..
IMPORTANT: Even if there is no registration fee we kindly ask you to register by filling the following
registration form:in word format
registration form: in pdf format
and send it to our technical secretary at
symplectic.geometry@gmail.com
This is because of two reasons: On the one hand, you will only get coffeee breaks and lunch if you register. On the other hand, this
conference is supported by the European Science Foundation and we have been asked to include information about participants that will be
of internal use for the ESF. Organizers and speakers are registered by default.
Grants:
There is a limited number of lodging grants. Preference will be given to Ph.D students and young postdocs. If you are interested in
applying for one of these grants please send your cv to eva.miranda@upc.edu no later than December 1st. The application for grants is
closed.
The grant holders will be lodged at the beautiful Residencia de Estudiantes. Residencia de Estudiantes is not a Student's Residence: it is
related to the movement of "Generacion del 27". You can learn about its history in the following link in wikipedia
:http://en.wikipedia.org/wiki/Residencia_de_Estudiantes
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/registration.htm[14/7/16 20:38:14]
Registration
Lodging:
Speakers and grant holders will be lodged either at the wonderful Residencia de Investigadores or at NH Zurbano.
Address of Residencia de Estudiantes:
Pinar, 21-23.
28006 Madrid
Phone: [+34] 91 563 64 11
http://www.residencia.csic.es/
How to get there?
http://www.residencia.csic.es/en/info/where.htm
Address of NH Zurbano:
http://www.nh-hoteles.es/nh/es/hoteles/espana/madrid/nh-zurbano.html
Zurbano, 79-81. 28003
Madrid
Tel. +34.91.4414500 | Fax: +34.91.4413224
Both hotels are located close to the stop Nuevos Ministerios. If you come by plane then the best thing to do is to take the metro and stop
at Nuevos Ministerios. The hotel is within a walking distance. A bus will be supplied by the organization to take you to ICMAT.
We kindly ask the rest of the particpants to book their own lodging. The following information might be useful:
For convenience of transportation, we recommend the area of Nuevos Ministerios or Chamartin.
List of hotels that we recommend:
Hotel NH Zurbano (in the Nuevos Ministerios area)
Registration
Hotel Suites Foxa 25 (in the Chamartin area) http://www.hotelesfoxa.com/Foxa25/
Hotel Suites Foxa 32 (in the Chamartin area
(http://www.hotelesfoxa.com/Foxa32/)
Other in-campus lodging: Residencia Erasmo. (student's residence)
http://www.resa.es/eng/Residencias/Erasmo/ubicacion
Other hotels:
http://www.madridhoteles.es/
The meeting will take place at ICMAT
C/ Nicolás Cabrera, nº 13-15
28049 Madrid
Funding
The conference is supported by:
- The European Science Foundation via CAST (Contact and Symplectic Topology)
- The ICMAT institute through the Severo Ochoa Programme.
- MICINN: Ministerio de Ciencia e Innovacion.
Palacio Real in Madrid
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/funding.htm[14/7/16 20:38:23]
Funding
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/funding.htm[14/7/16 20:38:23]
organizers
Organizing committee
Frédéric Bourgeois (Brussels)
Tobias Ekholm (Uppsala)
Eva Miranda (Barcelona)
Francisco Presas (Madrid)
Claude Viterbo (Paris)
Jean-Yves Welschinger (Lyon)
De tuin der lusten by Hieronymus Bosch you can visit it at El Prado
Team of collaborators: Roger Casals, Hector Castejon
and
Romero Solha (we are including the pictures so you
can recognize them)
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/organizers.htm[14/7/16 20:39:25]
organizers
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/organizers.htm[14/7/16 20:39:25]
Programme
New! You can download the programme in pdf from this link: programme.pdf
LAST MINUTE CHANGE IN THE PROGRAMME: The speaker Alvarez-Paiva has been replaced by Florent Balacheff
Schedule:
The conference will start at 3pm on Thursday and will finish on Saturday before lunch. We kindly ask you to come to the registration desk at 2:15 to take your
Welcome package and get your lunch ticket for Friday. The talks will take place at Sala Azul.
Time
09:30-10:30
Thursday
10:30-11:00
11:00-12:00
12:10-13:10
Registration (2:15-3p.m)
15:00- 16:00
Karshon
16:00- 16:30
16:30- 17:30
Hyvrier
Friday
Balacheff
Coffee Break
Eynard-Bontemps
Lisi
LUNCH
Evans
Coffee Break
Espina
Programme:
Florent Balacheff (Lille)
Contact perturbation theory and a question of Viterbo
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/programme.htm[14/7/16 20:39:47]
Saturday
Georgieva
Coffee Break
Cretois
Mundet
Programme
Abstract: Over ten years ago Claude Viterbo asked whether the ball in $R^{2n}$ has the largest symplectic capacity among all convex bodies of a given volume. In this talk we
shall give various partial (affirmative) answers to this question by adapting the perturbative techniques of celestial mechanics to study the dynamics of Reeb flows.
Remi Cretois (Lyon)
Real automorphisms of a vector bundle and Cauchy-Riemann operators
Abstract: We consider a complex vector bundle N equipped with a real structure c_N over a real curve (\Sigma_g,c_\Sigma) of genus g. The set of all Cauchy-Riemann
operators on (N,c_N) is a contractible space. The determinant bundle over this space is a real line bundle whose fiber at given operator is its determinant. We will try to
describe the action
of the automorphism group of (N,c_N) on the orientations of the determinant bundle and show some consequences on the first
Stiefel-Whitney class of the moduli spaces of
real pseudo-holomorphic curves in a real symplectic manifold.
Jacqueline Espina (Lyon) The mean Euler characteristic of contact structures
Abstract: The mean Euler characteristic (MEC) of a contact manifold is an invariant that arises in contact homology. True to its name, the mean Euler characteristic is the
average alternating sum of the ranks of cylindrical or linearized contact homology. This is a powerful enough invariant to distinguish inequivalent contact structures within the
same homotopy class. We will give an expression of the MEC in terms of local properties (the Conley-Zehnder and mean indices) of closed Reeb orbits for a broad class of
contact manifolds, the the so-called asymptotically nite contact manifolds. This class is essentially closed under subcritical contact surgery and we will see that the MEC changes
under such surgery in a very simple way. Furthermore, we will give an expression for he mean Euler characteristic in the Morse-Bott case and calculate the MEC for some
examples.
Helene Eynard Bontemps (Paris)
Homotopy of codimension one foliations on 3-manifolds
Abstract: We are interested in the topology of the space of smooth codimension one foliations on a given closed 3-manifold. In 1969, J. Wood proved that any smooth plane
field on a closed 3-manifold can be deformed into a plane field tangent to a foliation. This fundamental result was then reproved and generalized by W. Thurston.
Programme
It is natural then to wonder whether two foliations whose tangent plane fields are homotopic can be connected by a path of foliations, or, in
other words, if there is actually a bijection between the (pathwise) connected components of the space of foliations on a given manifold and that of the space of plane fields.
In this talk, we will show that the answer is essentially yes. To that end, we will first present Thurston's construction, along with later works by A. Larcanché, who answered the
above question in the case of two sufficiently close taut foliations.
Jonathan Evans (Zurich) Quantum cohomology of twistor spaces
Abstract: Monotone symplectic (aka symplectic Fano) manifolds are pretty rare in the universe of all symplectic manifolds, in much the same way that Fano varieties or Riccipositive manifolds are rare. Positivity usually has strong implications for the underlying topology and one wonders if the same is true here. However, the twistor space of a
hyperbolic 2n-manifold M (n bigger than or equal to 3) was observed to be a monotone symplectic manifold by Fine and Panov in 2009 and these examples counter many of
one’s expectations of what a symplectic Fano manifold ought to look like. We explore the symplectic topology of these spaces (for the simplest case n=3) further by computing
their quantum cohomology ring and the self-Floer cohomology of certain natural (equally unexpected) monotone Lagrangian submanifolds (Reznikov Lagrangians) associated to
totally geodesic n-dimensional submanifolds of M. We will see evidence that there might be (yet more unusual) Lagrangians hiding in these spaces that we haven't yet observed.
Penka Georgieva( Princeton)
Orientability and Open Gromov-Witten Invariants
Abstract: I will first discuss the orientability of the moduli spaces of J-holomorphic maps with Lagrangian boundary conditions. It is known that these spaces are not always
orientable and I will explain what the obstruction depends on. Then, in the presence of an anti-symplectic involution on the target, I will give a construction of open GromovWitten disk invariants. This is a generalization to higher dimensions of the works of Cho and Solomon, and is related to the invariants defined by Welschinger.
Clement Hyvrier( Uppsala) On symplectic uniruling of Hamiltonian fibrations.
Programme
Abstract: A symplectic manifold is said to be symplectically uniruled if there is a non vanishing genus zero Gromov-Witten invariant with one point constraint. It is known that
symplectic uniruledness of a closed Hamiltonian fibration over a symplectic base is induced from symplectic uniruledness of its fiber. We will show, under some assumptions,
that the same applies when we require the base to be symplectically uniruled instead. As a consequence such fibrations verify the Weinstein conjecture for separating
hypersurfaces, due to work of Lu (following previous results of Hofer-Viterbo and Li-Tian).
Counting toric actions
Abstract: In how many different ways can a two-torus act on a given simply connected symplectic four-manifold? If the second Betti number is one or two, the answer has
been known
for a while. For a higher Betti number, our (``soft") proof that there are only finitely many inequivalent torus actions did not enable us to count these actions.
I will report on more recent work, in which we reduce this counting question to combinatorics by expressing the manifold as a symplectic
blowup in a way that is compatible with all the torus actions simultaneously. For this we use the theory of pseudoholomorphic curves. This work is joint with Liat Kessler and
Martin Pinsonnault.
Fillings of spinal open books
Abstract: A spinal open book on a contact manifold is a generalization of a supporting open book. Open books arise naturally as the boundary of a Lefschetz fibration over a
disk. Similarly, spinal open books arise as the boundary of a Lefschetz fibration over a more general surface
with boundary. I will describe how the existence of a spinal open book with a certain planarity condition allows us to classify strong
fillings. Applications include classifications of fillings of circle bundles with $S^1$ invariant contact structures. This is joint work
with Jeremy Van Horn-Morris and Chris Wendl.
Ignasi Mundet i Riera (Barcelona)
Loops of homeomorphims of adjoint orbits
Programme
Abstract: Let $G$ be a compact Lie group and let ${\mathcal O}\subset{\mathfrak g}$ be an adjoint orbit of $G$. Our aim is to talk about the proof that the morphism
$G\to\text{Homeo}({\mathcal O})$ given by the adjoint action induces a monomorphism of fundamental groups. This extends a problem considered about 30 years ago by
Weinstein,
who asked the analogous question when the homeomorphisms group is replaced by the group of Hamiltonian symplectomorphisms (Weinstein's question was answered partially
by Viñas and in a complete way by McDuff and Tolman). This is joint work with David Martínez-Torres.
Template design by
Six Shooter Media.
practical
NEW: Please download the practical information (survival kit) in this pdf file here.
This conference has no registration fee but requires registration. Please go to the link Registration if you have
not registered yet.
How to get there:
From the airport to your hotel ( NH Zurbano or Residencia de Estudiantes): It is quite simple. This can be done in two steps:
Step 1: Take the metro Line 8 at the airport and stop at the stop Nuevos Ministerios.
Step 2: If you are lodged at NH Zurbano then the hotel is in a walking distance (10 minutes aprox): Follow this google maps to
find your way: http://www.pagines.ma1.upc.edu/~miranda/castmeeting/practical.htm[14/7/16 20:40:09]
practical
Those of you lodged at Residencia de Investigadores, it is also in a walking distance please follow the following
link:http://www.residencia.csic.es/en/info/where.htm
From your hotel to the conference Venue: For your convenience, we have arranged it so that there will be a conference bus that will take
you back and forth at a specific timetable. if you want to get there on your own, please follow the instructions at:
http://www.icmat.es/en/facilities/howtoarrive
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/practical.htm[14/7/16 20:40:09]
practical
Grants:
There is a limited number of lodging grants. Preference will be given to Ph.D students and young postdocs. If you are interested
in applying for one of these grants please send your cv to eva.miranda@upc.edu no later than December 1st. The application
for grants is closed.
he grant holders will be lodged at the beautiful Residencia de Estudiantes. Residencia de Estudiantes is not a Student's Residence:
it is related to the movement of "Generacion del 27". You can learn about its history in the following link in wikipedia
:http://en.wikipedia.org/wiki/Residencia_de_Estudiantes
Lodging:
Speakers and grant holders will be lodged either at the wonderful Residencia de Investigadores or at NH Zurbano.
Pinar, 21-23.
28006 Madrid
Phone: [+34] 91 563 64 11
How to get there?
http://www.residencia.csic.es/en/info/where.htm
Zurbano, 79-81. 28003
Madrid
practical
Tel. +34.91.4414500 | Fax: +34.91.4413224
Both hotels are located close to the metro stop Nuevos Ministerios. If you come by plane then the best thing to do is to take
the metro and stop at Nuevos Ministerios. The hotel is within a walking distance. A bus will be supplied by the organization to
take you to ICMAT.
We kindly ask the rest of the particpants to book their own lodging. The following information might be useful:
For convenience of transportation, we recommend the area of Nuevos Ministerios or Chamartin.
List of hotels that we recommend:
Hotel NH Zurbano (in the Nuevos Ministerios area)
Hotel Suites Foxa 25 (in the Chamartin area) http://www.hotelesfoxa.com/Foxa25/
Hotel Suites Foxa 32 (in the Chamartin area
(http://www.hotelesfoxa.com/Foxa32/)
Other in-campus lodging: Residencia Erasmo. (student's residence)
http://www.resa.es/eng/Residencias/Erasmo/ubicacion
Other hotels:
http://www.madridhoteles.es/
The meeting will take place at ICMAT
practical
28049 Madrid
Daily transportation:
There will be a bus taking speakers, organizers and participants from the area of Nuevos Ministerios to the Conference Venue.
More information will be available soon.
Panoramic of Madrid:
http://es.wikipedia.org/wiki/Archivo:Panoramic_of_Madrid.jpg seen from the Buenavista hill (15 km to the
South).picture autor http://commons.wikimedia.org/wiki/User:Miguel303xm
Participants
List of participants (78 participants as of Jan. 31):
Jaume
Silvia
Chantraine
Romero
Ahmet
Frederic
Jonathan Roger
Hector
Vincent Silvain
Antonio
Viviana Alejandra
Georgios
Jovana
Wojciech
Max
Albin
Anahita
Jaqueline Jonathan David
Chiara
Helene
Balacheff
Daniel
David
Viktor
Agnes
Damien
Penka
Paolo
Emmanuel Jesus
Luis Ramon
Vincent Johannes Clemet Gutt
Zehmisch
Yael Jaroslav
Laurent
Laurent
Paolo
Samuel
Eva
Klaus
Simone Ignasi
Vicente
Klaus
Stana
Francisco
Cretois
Reza
Marcelo
Thomas
Ana Ceferino
Nermin
Sheila
Gilberto
Simon Felix
Daniele Egor
Oldrich
Benoit
Anne
Nicolas
Thomas
Jack Chris Jerby
Marco
Frol
Naim
Amoros
Anjos
Baptiste
Barbieri Solha
Beyaz
Bourgeois
Bowden
Casals Gutierrez
Castejon Diaz
Colin
Courte
De Nicola
Diaz
Dimitroglou Rizell
Djuretic
Domitrz
Dörner
Eriksson-Östman
Eslami Rad
Espina
Evans
Exposito
Eynard Bontemps
Florent
Fox
Frenkel
Fromm
Gadbled
Gayet
Georgieva
Ghiggini
Giroux
Gonzalo
Guijarro
Horvath
Humiliere
Huster
Hyvrier
Jean
Kai
Karshon
Kedra
La Fuente-Gravy
Lazzarini
Lisca
Lisi
Miranda
Mohnke
Monau
Mundet
Muñoz
Niederkrüger
Nikcevic Simic
Presas
Remi
Rezazadegan
Ribeiro De Resende Alves
Rot
Rovi
Ruiz
Salepci
Sandon
Sapano
Schatz
Schlenk
Sepe
Shelukhin Spacil
Tonnelier
Vaugon
Vichery
Vogel
Waldron
Wendl
Yochay
Zambon
Zapolsky
Zenaidi
http://www.pagines.ma1.upc.edu/~miranda/castmeeting/participants.htm[14/7/16 20:40:11]
UNIVERSITAT POLITECNICA DE CATALUNYA
Instituto Superior Técnico
Université Libre de Bruxelles
Universidad Politécnica de Catalunya
Middle East Technical University
Max Planck Institute for Mathematics
CSIC
Polytechnic University of Catalonia
Universite de Nantes
UMPA ens Lyon
CMUC University of Coimbra
UNIVERSIDAD NACIONAL DEL SUR
UPPSALA UNIVERSITY
University of Belgrade
Warsaw University of Technology
Universität zu Köln
UPPSALA UNIVERSITY
University Libre de Bruxelles (ULB)
University Lyon I
ETH Zurich
University of Copenhage
UNIVERSITY PARIS 6
University of Science and Technology of Lille
EUIT Industrial, Universidad Politécnica de Madrid
Université de Neuchâtel
HUMBOLDT UNIVERSITAET BERLIN
UNIVERSITY OF CAMBRIDGE
ICJ LYON 1
PRINCETON UNIVERSITY
CNRS and UNIVERSITé DE NANTES
UMPA ens Lyon
UAM
Universidad Autónoma de Madrid
Uppsala University
Université Paris 6
University of Hamburg
UNIVERSITY OF UPPSALA
NIVERSITé LIBRE DE BRUXELLES & UNIVERSITé DE STRASBOURG UNIVERSITÄT ZU KÖLN
University of Toronto
University of Aberdeen
UNIVERSITY PARIS VI
UNIVERSITY OF PISA
UNIVERSITAT POLITECNICA DE CATALUNYA
HUMBOLDT UNIVERSITAET BERLIN
VU UNiversity Amsterdam
Universitat de Barcelona
UNIVERSIDAD COMPLUTENSE DE MADRID
Universite de Tolouse III
Institute Mathematical SANLI
ICMAT
UNIVERSITE LYON 1
UNIVERSITé DE NANTES
VU University Amsterdam
UNIVERSITY OF GLASGOW
Universidad de Granada
University Lyon I
CNRS – Universite de Nantes and IAS Princeton
UNIVERSITé DE NANTES
Institut de Recherche en Mathematiqué Avancee
Université de Neuchatel
Centre for Mathematical Analysis, Geometry and Dynamical System
Tel Aviv University, Israel
UNIVERSITY OF ABERDEEN
Ens de Lyon
Universite de Nantes
ENS (Paris)
Max Planck Institute for Mathematics
UNIVERSITY OF OXFORD
University College London
Neuchatel University, Switzerland
UNIVERSIDAD AUTONOMA DE MADRID-ICMAT
LMU MUNICH
ULB (Brusells)
VI Workshop on Symplectic Geometry,
Contact Geometry and Interactions
ICMAT, Madrid February 2-4, 2012
Programme
Conference supported by
ESF via CAST
ICMAT via the Severo Ochoa Programme
MICINN, Ministerio de Ciencia e Innovación
List of speakers:
Juan-Carlos Álvarez-Paiva (Lille)
Rémi Cretois (Lyon)
Jacqueline Espina (Lyon)
Hélène Eynard-Bontemps (Paris)
Penka Georgieva (Princeton)
Clément Hyvrier (Uppsala)
Ignasi Mundet i Riera (Barcelona)
Schedule:
The conference will start at 3pm on Thursday and will finish on Saturday
before lunch. We kindly ask you to come to the registration desk at 2:15
to take your Welcome package and get your lunch ticket for Friday.
Time
Thursday
Friday
Saturday
09:30-10:30
Alvarez-Paiva
Georgieva
10:30-11:00
Coffee Break
Coffee Break
11:00-12:00
Eynard-Bontemps
Cretois
12:10-13:10
Lisi
Mundet
Registration (2:15-3p.m)
15:00- 16:00
Karshon
Evans
Coffee Break
16:00- 16:30
16:30- 17:30
LUNCH
Hyvrier
Espina
Programme:
Juan Carlos Álvarez-Paiva (Lille) Contact perturbation theory
and a question of Viterbo
Abstract:
Over ten years ago Claude Viterbo asked whether the ball in
$R^{2n}$ has the largest symplectic capacity among all convex bodies of a
given volume. In this talk we shall give various partial (affirmative) answers to
this question by adapting the perturbative techniques of celestial mechanics to
study the dynamics of Reeb flows.
Rémi Cretois (Lyon) Real automorphisms of a vector bundle
and Cauchy-Riemann operators
Abstract:
We consider a complex vector bundle N equipped with a real
structure c_N over a real curve (\Sigma_g,c_\Sigma) of genus g. The set of all
Cauchy-Riemann operators on (N,c_N) is a contractible space. The determinant
bundle over this space is a real line bundle whose fiber at given operator is its
determinant. We will try to describe the action of the automorphism group of
(N,c_N) on the orientations of the determinant bundle and show some
consequences on the first Stiefel-Whitney class of the moduli spaces of real
pseudo-holomorphic curves in a real symplectic manifold.
Jacqueline Espina (Lyon) The mean Euler characteristic of
contact structures
Abstract:
The mean Euler characteristic (MEC) of a contact manifold is an
invariant that arises in contact homology. True to its name, the mean Euler
characteristic is the average alternating sum of the ranks of cylindrical or
linearized contact homology. This is a powerful enough invariant to distinguish
inequivalent contact structures within the same homotopy class. We will give an
expression of the MEC in terms of local properties (the Conley-Zehnder and
mean indices) of closed Reeb orbits for a broad class of contact manifolds, the
the so-called asymptotically nite contact manifolds. This class is essentially
closed under subcritical contact surgery and we will see that the MEC changes
under such surgery in a very simple way. Furthermore, we will give an
expression for he mean Euler characteristic in the Morse-Bott case and
calculate the MEC for some examples.
spaces
Quantum cohomology of twistor
Abstract: Monotone symplectic (aka symplectic Fano) manifolds are pretty rare
in the universe of all symplectic manifolds, in much the same way that Fano
varieties or Ricci-positive manifolds are rare. Positivity usually has strong
implications for the underlying topology and one wonders if the same is true
here. However, the twistor space of a hyperbolic 2n-manifold M (n bigger than
or equal to 3) was observed to be a monotone symplectic manifold by Fine and
Panov in 2009 and these examples counter many of one’s expectations of what
a symplectic Fano manifold ought to look like. We explore the symplectic
topology of these spaces (for the simplest case n=3) further by computing their
quantum cohomology ring and the self-Floer cohomology of certain natural
(equally
unexpected)
monotone
Lagrangian
submanifolds
(Reznikov
Lagrangians) associated to totally geodesic n-dimensional submanifolds of M.
We will see evidence that there might be (yet more unusual) Lagrangians hiding
in these spaces that we haven't yet observed.
Hélène Eynard-Bontemps (Paris) Homotopy of codimension
one foliations on 3-manifolds
We
are
interested
codimension
one
in
the
foliations
topology
on
a
of
the
given
space
closed
of
smooth
3-manifold.
In 1969, J. Wood proved that any smooth plane field on a closed
3-manifold can be deformed into a plane field tangent to a foliation.
This fundamental result was then reproved and generalized by W.
Thurston.
It is natural then to wonder whether two foliations whose tangent plane
fields are homotopic can be connected by a path of foliations, or, in
other words, if there is actually a bijection between the (pathwise)
connected components of the space of foliations on a given manifold and
that
of
the
space
of
plane
fields.
In this talk, we will show that the answer is essentially yes. To that
end,
we
will
first
present
Thurston's
construction,
along
with
later
works by A. Larcanché, who answered the above question in the case of
two sufficiently close taut foliations.
Penka Georgieva (Princeton) Orientability and Open GromovWitten Invariants
Abstract:
I will first discuss the orientability of the moduli spaces of J-
holomorphic maps with Lagrangian boundary conditions. It is known that these
spaces are not always orientable and I will explain what the obstruction
depends on. Then, in the presence of an anti-symplectic involution on the
target, I will give a construction of open Gromov-Witten disk invariants. This is a
generalization to higher dimensions of the works of Cho and Solomon, and is
related to the invariants defined by Welschinger.
Clément Hyvrier (Uppsala)
Hamiltonian fibrations.
On
symplectic
uniruling
of
Abstract: A symplectic manifold is said to be symplectically uniruled if there is
a non vanishing genus zero Gromov-Witten invariant with one point constraint.
It is known that symplectic uniruledness of a closed Hamiltonian fibration over a
symplectic base is induced from symplectic uniruledness of its fiber. We will
show, under some assumptions, that the same applies when we require the
base to be symplectically uniruled instead. As a consequence such fibrations
verify the Weinstein conjecture for separating hypersurfaces, due to work of Lu
(following previous results of Hofer-Viterbo and Li-Tian).
Yael Karshon (Toronto) Counting toric actions
Abstract: In how many different ways can a two-torus act on a given simply
connected symplectic four-manifold? If the second Betti number is one or two,
the answer has been known for a while. For a higher Betti number, our (``soft")
proof that there are only finitely many inequivalent torus actions did not enable
us to count these actions.
I will report on more recent work, in which we reduce this counting question to
combinatorics by expressing the manifold as a symplectic
blowup in a way that is compatible with all the torus actions simultaneously. For
this we use the theory of pseudoholomorphic curves. This work is joint with Liat
Kessler and Martin Pinsonnault.
Samuel Lisi (Brussels) Fillings of spinal open books
Abstract: A spinal open book on a contact manifold is a generalization of a
supporting open book. Open books arise naturally as the boundary of a
Lefschetz fibration over a disk. Similarly, spinal open books arise as the
boundary of a Lefschetz fibration over a more general surface
with boundary. I will describe how the existence of a spinal open book with a
certain planarity condition allows us to classify strong
fillings. Applications include classifications of fillings of circle bundles with
$S^1$ invariant contact structures. This is joint work
with Jeremy Van Horn-Morris and Chris Wendl.
Ignasi Mundet i Riera (Barcelona) Loops of homeomorphims of
adjoint orbits
Abstract:
Let
$G$
be
a
compact
Lie
group
and
let
${\mathcal
O}\subset{\mathfrak g}$ be an adjoint orbit of $G$. Our aim is to talk about the
proof that the morphism $G\to\text{Homeo}({\mathcal O})$ given by the adjoint
action induces a monomorphism of fundamental groups. This extends a
problem considered about 30 years ago by Weinstein, who asked the
analogous question when the homeomorphisms group is replaced by the group
of Hamiltonian symplectomorphisms (Weinstein's question was answered
partially by Viñas and in a complete way by McDuff and Tolman). This is joint
work with David Martínez-Torres.
VI Workshop on Symplectic Geometry,
Contact Geometry and Interactions
ICMAT, Madrid February 2-4, 2012
Survival Kit
How to get to the hotels:
•
From the airport to your hotel ( NH Zurbano or
Residencia de Estudiantes) : It is quite simple. This can be
done in two steps:
o Step 1: Take the metro Line 8 at the airport and stop at the stop
Nuevos Ministerios.
o Step 2:
 If you are lodged at NH Zurbano then the hotel is in a
walking distance (10 minutes aprox): Follow this google
maps to find your way:
• Those of you lodged at Residencia de Investigadores, it is
also in a walking distance please follow the following
link:http://www.residencia.csic.es/en/info/where.htm
Pinar, 21-23.
28006 Madrid
Phone: [+34] 91 563 64 11
Zurbano, 79-81. 28003 Madrid
Tel. +34.91.4414500 | Fax: +34.91.4413224
To get to the conference (ICMAT building)
A) Official bus:
Schedule:
Thursday 13:30 Madrid- ICMAT
Thursday 17:45 ICMAT-Madrid
Friday 8:45 Madrid-ICMAT
Friday 17:45 ICMAT-Madrid
Saturday 8:45 Madrid-ICMAT
SAturday 13:15 ICMAT-Madrid
Meeting point (in Madrid): Plaza San Juan de la Cruz
Walking from te hotel:
Walking from the Residence:
B) Public transportation:
TRAIN
Take the RENFE Cercanías train C4 line (either Alcobendas direction or Colmenar
Viejo direction). Get off at Cantoblanco Universidad station and go straight ahead
Francisco Tomás y Valiente street. The ICMAT is at the end of this street just on the
intersection with 13-15 Nicolás Cabrera St.
BUS
There are several intercity bus lines, for instance:
Nr. 714, from Madrid (Castilla Square bus exchanger) to Cantoblanco Campus
(Centro Nacional de Biotecnología stop) and then walk five minutes through Francisco Tomás y Valiente St. passing by Escuela Politécnica Superior.
Nr. 827, Canillejas / Alcobendas – UAM Cantoblanco / Tres Cantos.
Nr. 827-A, San Sebastian de los Reyes / Alcobendas – UAM Cantoblanco.
Nr. 828, Campo de las Naciones – Barajas Airport (T4) – UAM Cantoblanco.
You can check the timetables corresponding to the different bus lines, by clicking
the link.
* Notice that neither 714 nor 827 bus goes to UAM Cantoblanco on Sundays or
holidays.
* 827-A and 828 bus lines provide service only on weekdays!
For further information, visit this website link belonging to the University.
CAR
The easiest way for arriving by private transport or taxi is through the UAM Northern access, via M-607 dual carriageway (from Madrid to Colmenar Viejo) combined with M-616 road (from El Pardo to Alcobendas).
Once you get into the Cantoblanco Campus, follow Erasmo de Rotterdam St. on
the left direction, turn right on Newton St. and then take the first turning on the
left, which is Nicolás Cabrera St.
There are parking facilities at the end of the street.
ICMAT location (red marker)
Inside the whole campus:
Local picture:
Registration for the Workshop on Symplectic Geometry, Contact
Geometry and Interactions.
Please write in capital letters and send this form to the technical SecretariatYou can send by e-mail or by fax: +34 915217964.
azafatasycongresos@gmail.com
symplectic.geometry@gmail.com
The following information will be included in a file for the European Science Foundation.
SURNAME:____________________________________NAME:___________________________
DATE OF BIRTH:_______________________________NATIONALITY:____________________
INSTITUTION:________________________________________________________________
DEPARTMENT:________________________________________________________________
INSTITUTION ADRESS: ________________________________________________________
CITY:________________________________ ZIP:____________COUNTRY:________________
PHONE:_____________________________ FAX NUMBER:______________________________
E-MAIL:______________________________________________________________________
WEB:________________________________________________________________________
Coffee breaks will be provided for free for registered participants on Thursday, Friday and Saturday.
Lunch will be provided for free for registered participants on Friday. We need to know if you have some dietary
constraints.
Indicate them here if any:
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
Please tick the right item:
-I have applied for a lodging grant YES NO
Don’t forget to send your cv to eva.miranda@upc.edu if you wish to be eligible for one.
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Workshop on Symplectic Geometry, Contact Geometry and

Transcription

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