Attendance to this advanced school will also be available online (except for the problem sessions). If you with to attend online, please select the relevant option during the registration process.
Poisson 2022 Advanced School
to July 22, 2022
Please, stay in this webpage if you are registering just for the Poisson 2022 Advanced School taking place at the CRM or if you are applying for a grant.
The Summer School on Poisson Geometry aims to introduce the participants to Poisson Geometry and related fields, as well as to present some of the most recent developments and open problems in the field. The targeted audience is final-year undergraduate students, graduate students and young researchers. The only required background is basic differential geometry.
The school will consist of four minicourses during one week. There will be problems sessions to promote the participation of the students of the school, and also several activities to foster social interaction.
This school will be followed by a week-long conference which will take place in Madrid.
There will be a topical Issue on the Journal of Geometry and Physics dedicated to Poisson Geometry in Mathematics and Physics.
Editors: Anton Alekseev, Lisa Jeffrey, Eva Miranda and Volodya Roubtsov
(more information will be posted soon)
About Poisson Geometry
Poisson Geometry lies on the crossroads of Mathematical Physics and Geometry. It originates in the mathematical formulation of Hamiltonian mechanics and as the semiclassical limit of quantum systems. Although Poisson structures can be traced back to some of the classical works of the 19th century (Poisson, Hamilton, Jacobi, Lie), Poisson Geometry started as a field around 1980 with the work of Lichnerowicz, Weinstein, etc. The field developed rapidly, stimulated by the connections with a large number of areas in mathematics and mathematical physics, including differential geometry and Lie theory, quantization, noncommutative geometry, representation theory and quantum groups, geometric mechanics, and integrable systems.
Lecturer: Ana Balibanu (Harvard)
Chair: Jiang-Hua Lu (Hong Kong)
Abstract: Every complex semisimple group of adjoint type has a canonical, smooth compactification which encodes the asymptotic behavior of the group “at infinity.” It is constructed using representation-theoretic data, and its geometry is indexed by the combinatorics of the corresponding root system. This course will outline some of the remarkable properties of this algebraic variety, and some of its many applications.
Lecture 1: Outline of the construction. Structure theory of the wonderful compactification, its boundary divisor, and distinguished subvarieties.
Lecture 2: Poisson structures associated to the compactification. Poisson homogeneous spaces and the variety of Lagrangian subalgebras.
Lecture 3: Current developments, additive analogues, and connections to combinatorics and algebraic geometry.
Introduction to Poisson Geometry
Lecturer: Henrique Bursztyn (IMPA)
Chair: Eckhard Meinrenken (Toronto)
Abstract: This mini-course will offer a panoramic view of Poisson geometry, including both classical aspects and modern developments of the theory.
We will start with basic definitions and concepts related to Poisson structures, some foundational results (local theory, symplectic leaves) and key examples. We will then discuss symplectic groupoids and more general connections with Lie groupoids and multiplicative geometric structures. I will also introduce Dirac structures, their main properties and various applications, both within and beyond Poisson geometry.
Lecturer: Camille Laurent-Gengoux (Metz)
Chair: Rui Fernandes (Urbana-Champaign)
Abstract: Foliations are partitions of a manifold into sub-manifolds called leaves. They are said to be singular when the dimension all some leaves are not constant. Orbits of Lie group actions, symplectic leaves of a Poisson bivector, symmetries of affine varieties are among examples. I will try to give a detailed proof of several basic but subtle theorems about singular foliations and to give an overview of the geometry of their singular leaves.
Lecture 1: Discussion of the various possible definitions of singular foliation. Examples and counter examples. Existence of leaves and local splitting theorem.
Lecture 2: Various algebraic or geometric structures hidden behind a singular foliation: holonomy Lie algebras, holonomy groupoids. Bi-submersions and first-return.
Lecture 3: Open (and closed) questions from algebraic and differential geometry to theoretical physics.
A problem session will take place after Lecture 2.
Geometric quantization, old and new
Lecturer: Jonathan Weitsman (Northeastern University)
Chair: Chenchang Zhu (Goettingen)
Abstract: We give an overview of Geometric Quantization, with an emphasis on examples and on invariance of polarization, and on applications to analysis and representation theory. We then study recent extensions of the theory which apply to the a class of Poisson manifolds, the b-symplectic manifolds, when equipped with Hamiltonian torus actions.
REGISTRATION FEE FOR ON-SITE PARTICIPATION: 200€*
* includes reception, coffee breaks, daily lunch and a guided visit to Barcelona.
If you wish to register for the POISSON Advanced School, please click on the SIGN IN botton.
* Due to space limitations, registration will be served on first-come first-served basis (maximum attendance 100 participants)
REGISTRATION FEE FOR ON-LINE PARTICIPATION: 0€ (Registration for online participants is free but mandatory in order to have access to the ZOOM link for the sessions)
advanced school & the conference
You can register for both activities, the Poisson Advanced School taking place at the CRM from 18-22 July 2022 and the Poisson Conference, taking place at the ICMAT from 25-29 July 2022.
COMBINED REGISTRATION FEE: 300€
The combined registration covers:
- For the Advanced Course: reception, coffee breaks, daily lunch and a guided visit to Barcelona.
- For the Poisson 2022 Conference: reception, coffee breaks and conference dinner.
* If you wish to apply for a grant for the Advanced Course, you will need to register separately through this website and through the conference website (click here)
REGISTRATION TO BOTH ACTIVITIES
- Application deadline is May 15, 2022
- Resolutions will be sent by June 02, 2022
* grants cover everything included with the registration (reception, coffee breaks, daily lunch and a guided visit to Barcelona).
IF YOUR INSTITUTION COVERS YOUR REGISTRATION FEE: Please note that, in case your institution is paying for the registration via bank transfer, you will have to indicate your institution details and choose “Transfer” as the payment method at the end of the process.
UPF | UB | UPC | UAB
*If the paying institution is the UPF / UB/ UPC / UAB, after registering, please send an email to email@example.com with your name and the institution internal reference number that we will need to issue the electronic invoice. Please, send us the Project code covering the registration if needed.
*If the paying institution is IDIBAPS, please send an email to firstname.lastname@example.org with the Project reference code that will cover the registration cost, to be added to the invoice if necessary.
Paying by credit card
IF YOU PAY VIA CREDIT CARD but you need to provide the invoice to your institution to be reimbursed, please note that we will also need you to send an email to email@example.com providing the internal reference number given by your institution and the code of the Project covering the registration (if necessary).
If you are not applying for a grant, here you can find some options regarding accommodation during the event.
ON-CAMPUS AND BELLATERRA
BARCELONA AND OFF-CAMPUS
LIST OF PARTICIPANTS OF THE ADVANCED COURSE
|Yu Li||Max Planck Institute for Mathematics|
|Thiago Paulichen||Universidade Federal do Paraná|
|Henrique Bursztyn||Instituto Nacional de Matematica Pura e Aplicada|
|Kentaro Mikami||Akita University|
|Anna Blanco Cabanillas||Universitat de Barcelona|
|Pau Mir||Universitat Politècnica de Catalunya|
|King Leung Lee||Universidad Autónoma de Madrid|
|Aldo Witte||Katholieke Universiteit Leuven|
|Ismael Ahlouche||University of Mons|
|Jair Koiller||Federal University of Rio de Janeiro|
|Luis P. Yapu Quispe||Federal University of Rio de Janeiro|
|Matthew Koster||University of Toronto|
|Nan Li||Shanghai Jiao Tong University|
|Ruben LOUIS||University of Lorraine|
|Véronique Chloup||University of Lorraine|
|Cédric Oms||École normale supérieure de Lyon|
|Cédric Oms||École normale supérieure de Lyon|
|Fabio Gironella||Humboldt University of Berlin|
|Lory Kadiyan||University of Bonn|
|Sourav Das||University of Haifa|
|Margherita De Fata||Sapienza University of Rome|
|Noriaki Ikeda||Ritsumeikan University|
|Paulina Pierzchala||AGH University of Science and Technology|
|Lennart Obster||University of Coimbra|
|Yunhyung Cho||Sungkyunkwan University|
|Rea Dalipi||Swiss Federal Institute of Technology in Zurich|
|Ana Balibanu||Harvard University|
|Pallav Goyal||University of Chicago|
|Aline Leite Vilela D\\\'Oliveira||University of Illinois at Urbana–Champaign|
LIST OF PARTICIPANTS OF THE ADVANCED COURSE AND THE CONFERENCE
|David Baldomero Iglesias Ponte||Universidad de la Laguna|
|Alice Barbora Tumpach||University of Vienna|
|Pacôme Van Overschelde||Université libre de Bruxelles|
|Marta Farre Puiggali||University of Antwerp|
|Ioan Marcut||Radboud University Nijmegen|
|Milan Niestijl||Delft University of Technology|
|Joao Nuno Mestre||University of Coimbra|
|Byunghee An||Kyungpook National University|
|Jin Hong Kim||Chosun University|