HYBRID ACTIVITY

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.

SCHEDULE

Poisson 2022 Advanced School

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Advanced course / School
From July 18, 2022
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.

Registration deadline 26 / 06 / 2022

Description

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.

Lecturers

Wonderful Compactifications

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.

Singular Foliations

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

advanced school

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

Grants

The organisation offers registration and accommodation grants for participants. To apply, please register for the activity through SIGN IN and choose “reservation” as the payment method at the end of the process. You will be asked to upload your CV. Resolutions will be sent by the end of May and candidates will be informed about how to finalise the process.
    • 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).

Organizers

Mario García Fernández (ICMAT–UAM)

David Iglesias Ponte (La Laguna)

David Martín de Diego (ICMAT–CSIC)

Anastasiia Matveeva (UPC)

Eva Miranda (UPC-CRM) – Chair

Cédric Oms (UPC)

Daniel Peralta-Salas (ICMAT–CSIC)

Roberto Rubio (UB)

Scientific committee

Chenchang Zhu (Goettingen) – Chair

Anton Alekseev (Geneva)

Henrique Bursztyn (IMPA)

Rui Loja Fernandes (Urbana-Champaign)

Eckhard Meinrenken (Toronto)

Jiang-Hua Lu (Hong Kong)

INVOICE/PAYMENT INFORMATION

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 vramirez@crm.cat 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.

IDIBAPS

*If the paying institution is IDIBAPS, please send an email to vramirez@crm.cat 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 vramirez@crm.cat providing the internal reference number given by your institution and the code of the Project covering the registration (if necessary).

Lodging information

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

Name Institution
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

Name Institution
Ana Mançur IMPA
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

Acknowledgements

 

For inquiries about this event please contact the research programs coordinator Ms. Núria Hernández at nhernandez@crm.cat​​