Summer School and Conference on Poisson Geometry

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Summer School and Conference on Poisson Geometry | (smr 1665)

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Monday, 4 July 2005

08:30 - 10:30 REGISTRATION AND ADMINISTRATIVE FORMALITIES

Location: Adriatico Guest House (Lower Level 1)
- 08:30 REGISTRATION AND ADMINISTRATIVE FORMALITIES 2h0'
10:30 - 10:45 OPENING
- 10:30 OPENING 15'

10:45 - 12:00 Symmetry and reduction in Poisson Geometry, I

10:45 Symmetry and reduction in Poisson Geometry, I 1h15'

Speaker:	J.P. Ortega (Université de Franche-Comte, Besançon, France)
Material:	lecture notes

12:00 - 14:00 Lunch Break
- 12:00 Lunch Break 2h0'

14:00 - 15:00 Normal forms of Poisson structures, I

14:00 Normal forms of Poisson structures, I 1h0'

Speaker:	J.P. Dufour (Université Montpellier II, Montpellier, France)
Material:	lecture notes

15:00 - 15:20 Break
- 15:00 Break 20'

15:20 - 16:20 Applications of Poisson geometry to physical problems, I

15:20 Applications of Poisson geometry to physical problems, I 1h0'

Speaker:	D. Holm (Imperial College, London, UK.)
Material:	lecture notes

16:20 - 16:45 Break
- 16:20 Break 25'

16:45 - 18:00 Supersymmetric mechanics and functional integration, I

16:45 Supersymmetric mechanics and functional integration, I 1h15'

Speaker:	P. Cartier (IHES, France)
Material:	lecture notes

Tuesday, 5 July 2005

08:45 - 10:00 Symmetry and reduction in Poisson Geometry, II
- 08:45 Symmetry and reduction in Poisson Geometry, II 1h15'
  
  Speaker: J.P. Ortega (Université de Franche-Comte, Besançon, France)
10:00 - 10:30 Break
- 10:00 Break 30'

10:30 - 12:00 Dirac structures, I

10:30 Dirac structures, I 1h30'

Speaker:	G. Blankenstein/T. Ratiu (Katholieke Universiteit Leuven, Belgium/E.P.F.L., Lausanne, Switzerland)
Material:	lecture notes

12:00 - 14:00 Lunch Break
- 12:00 Lunch Break 2h0'
14:00 - 15:00 Normal forms of Poisson structures, II
- 14:00 Normal forms of Poisson structures, II 1h0'
  
  Speaker: J.P. Dufour (Université Montpellier II, Montpellier, France)
15:00 - 15:20 Break
- 15:00 Break 20'
15:20 - 16:20 Applications of Poisson geometry to physical problems, II
- 15:20 Applications of Poisson geometry to physical problems, II 1h0'
  
  Speaker: D. Holm (Imperial College, London, UK.)
16:20 - 16:45 -
- 16:20 - 25'
16:45 - 18:00 Supersymmetric mechanics and functional integration, II
- 16:45 Supersymmetric mechanics and functional integration, II 1h15'
  
  Speaker: P. Cartier (IHES, France)

Wednesday, 6 July 2005

08:45 - 10:00 Symmetry and reduction in Poisson Geometry, III
- 08:45 Symmetry and reduction in Poisson Geometry, III 1h15'
  
  Speaker: J.P. Ortega (Université de Franche-Comte, Besançon, France)
10:00 - 10:30 Break
- 10:00 Break 30'

10:30 - 12:00 Dirac structures, II

10:30 Dirac structures, II 1h30'

Speaker:	G. Blankenstein/T. Ratiu (Katholieke Universiteit Leuven, Belgium/E.P.F.L., Lausanne, Switzerland)
Material:	lecture notes

12:00 - 14:00 Lunch Break
- 12:00 Lunch Break 2h0'
14:00 - 15:00 Normal forms of Poisson structures, III
- 14:00 Normal forms of Poisson structures, III 1h0'
  
  Speaker: J.P. Dufour (Université Montpellier II, Montpellier, France)
15:00 - 15:20 Break
- 15:00 Break 20'
15:20 - 16:20 Applications of Poisson geometry to physical problems, III
- 15:20 Applications of Poisson geometry to physical problems, III 1h0'
  
  Speaker: D. Holm (Imperial College, London, UK.)
16:20 - 16:45 Break
- 16:20 Break 25'
16:45 - 18:00 Supersymmetric mechanics and functional integration, III
- 16:45 Supersymmetric mechanics and functional integration, III 1h15'
  
  Speaker: P. Cartier (IHES, France)

Thursday, 7 July 2005

08:45 - 10:00 Symmetry and reduction in Poisson Geometry, IV
- 08:45 Symmetry and reduction in Poisson Geometry, IV 1h15'
  
  Speaker: J.P. Ortega (Université de Franche-Comte, Besançon, France)
10:00 - 10:30 Break
- 10:00 Break 30'

10:30 - 12:00 Dirac structures, III

10:30 Dirac structures, III 1h30'

Speaker:	G. Blankenstein/T. Ratiu (Katholieke Universiteit Leuven, Belgium/E.P.F.L., Lausanne, Switzerland)
Material:	lecture notes

12:00 - 14:00 Lunch Break
- 12:00 Lunch Break 2h0'
14:00 - 15:00 Normal forms of Poisson structures, IV
- 14:00 Normal forms of Poisson structures, IV 1h0'
  
  Speaker: N.T. Zung (Université Paul Sabatier, Toulouse, France)
15:00 - 15:20 Break
- 15:00 Break 20'
15:20 - 16:20 Applications of Poisson geometry to physical problems, IV
- 15:20 Applications of Poisson geometry to physical problems, IV 1h0'
  
  Speaker: D. Holm (Imperial College, London, UK.)
16:20 - 16:45 Break
- 16:20 Break 25'
16:45 - 18:00 Lie groupoids and Lie algebroids, I: Lie groupoids
- 16:45 Lie groupoids and Lie algebroids, I: Lie groupoids 1h15'
  
  Speaker: M. Crainic (Utrecht University, Utrecht, The Netherlands)

Friday, 8 July 2005
- 08:45 - 10:00 Supersymmetric mechanics and functional integration, IV
  - 08:45 Supersymmetric mechanics and functional integration, IV 1h15'
    
    Speaker: P. Cartier (IHES, France)
- 10:00 - 10:30 Break
  - 10:00 Break 30'
- 10:30 - 12:00 Dirac structures, IV
  - 10:30 Dirac structures, IV 1h30'
    
    Speaker: G. Blankenstein/T. Ratiu (Katholieke Universiteit Leuven, Belgium/E.P.F.L., Lausanne, Switzerland)
- 12:00 - 14:00 Lunch Break
  - 12:00 Lunch Break 2h0'
- 14:00 - 15:00 Normal forms of Poisson structures, V
  - 14:00 Normal forms of Poisson structures, V 1h0'
    
    Speaker: N.T. Zung (Université Paul Sabatier, Toulouse, France)
- 15:00 - 15:20 Break
  - 15:00 Break 20'
- 15:20 - 16:20 Applications of Poisson geometry to physical problems, V
  - 15:20 Applications of Poisson geometry to physical problems, V 1h0'
    
    Speaker: D. Holm (Imperial College, London, UK.)
- 16:20 - 16:45 Break
  - 16:20 Break 25'
- 16:45 - 18:00 Lie groupoids and Lie algebroids, II: Lie algebroids
  - 16:45 Lie groupoids and Lie algebroids, II: Lie algebroids 1h15'
    
    Speaker: R. L. Fernandes (Instituto Superior Tecnico, Lisbon, Portugal)

Monday, 11 July 2005

08:45 - 09:45 Quantization of Poisson manifolds, I

08:45 Quantization of Poisson manifolds, I 1h0'

Speaker:	S. Gutt (Université Libre de Bruxelles, Bruxelles, Belgique)
Material:	lecture notes

09:45 - 10:00 Break
- 09:45 Break 15'

10:00 - 11:00 Bihamiltonian structures and Frobenius manifolds, I

10:00 Bihamiltonian structures and Frobenius manifolds, I 1h0'

Speaker:	B. Dubrovin (SISSA, Trieste, Italy)
Material:	lecture notes

11:00 - 11:20 Break
- 11:00 Break 20'

11:20 - 12:20 Infinite dimensional Poisson geometry and coherent states, I

11:20 Infinite dimensional Poisson geometry and coherent states, I 1h0'

Speaker:	A. Odzijewicz (University of Bialystok, Bialystok, Poland)
Material:	lecture notes

12:20 - 14:30 Lunch Break
- 12:20 Lunch Break 2h10'
14:30 - 15:45 Lie groupoids and Lie algebroids, III: integrability theorem
- 14:30 Lie groupoids and Lie algebroids, III: integrability theorem 1h15'
  
  Speaker: M. Crainic (Utrecht University, Utrecht, The Netherlands)
15:45 - 16:15 Break
- 15:45 Break 30'
16:15 - 17:30 Lie groupoids and Lie algebroids, IV: integrability theorem
- 16:15 Lie groupoids and Lie algebroids, IV: integrability theorem 1h15'
  
  Speaker: R. L. Fernandes (Instituto Superior Tecnico, Lisbon, Portugal)

Tuesday, 12 July 2005

08:45 - 09:45 Quantization of Poisson manifolds, II
- 08:45 Quantization of Poisson manifolds, II 1h0'
  
  Speaker: S. Gutt (Université Libre de Bruxelles, Bruxelles, Belgique)
09:45 - 10:00 Break
- 09:45 Break 15'

10:00 - 11:00 Bihamiltonian structures and Frobenius manifolds, II

10:00 Bihamiltonian structures and Frobenius manifolds, II 1h0'

Speaker:	B. Dubrovin (SISSA, Trieste, Italy)
Material:	lecture notes

11:00 - 11:20 Break
- 11:00 Break 20'
11:20 - 12:20 Infinite dimensional Poisson geometry and coherent states, II
- 11:20 Infinite dimensional Poisson geometry and coherent states, II 1h0'
  
  Speaker: A. Odzijewicz (University of Bialystok, Bialystok, Poland)
12:20 - 14:30 Lunch Break
- 12:20 Lunch Break 2h10'

14:30 - 15:45 Poisson-Lie groups and Poisson groupoids, I

14:30 Poisson-Lie groups and Poisson groupoids, I 1h15'

Speaker:	P. Xu (The Pennsylvania State University, State College, USA)
Material:	lecture notes

15:45 - 16:15 Break
- 15:45 Break 30'
16:15 - 17:30 Lie groupoids and Lie algebroids, V: integrability and prequantization
- 16:15 Lie groupoids and Lie algebroids, V: integrability and prequantization 1h15'
  
  Speaker: M. Crainic (Utrecht University, Utrecht, The Netherlands)

Wednesday, 13 July 2005

08:45 - 09:45 Quantization of Poisson manifolds, III
- 08:45 Quantization of Poisson manifolds, III 1h0'
  
  Speaker: S. Gutt (Université Libre de Bruxelles, Bruxelles, Belgique)
09:45 - 10:00 Break
- 09:45 Break 15'

10:00 - 11:00 Bihamiltonian structures and Frobenius manifolds, III

10:00 Bihamiltonian structures and Frobenius manifolds, III 1h0'

Speaker:	B. Dubrovin (SISSA, Trieste, Italy)
Material:	lecture notes

11:00 - 11:20 Break
- 11:00 Break 20'
11:20 - 12:20 Infinite dimensional Poisson geometry and coherent states, III
- 11:20 Infinite dimensional Poisson geometry and coherent states, III 1h0'
  
  Speaker: A. Odzijewicz (University of Bialystok, Bialystok, Poland)
12:20 - 14:30 Lunch Break
- 12:20 Lunch Break 2h10'
14:30 - 15:45 Poisson-Lie groups and Poisson groupoids, II
- 14:30 Poisson-Lie groups and Poisson groupoids, II 1h15'
  
  Speaker: P. Xu (The Pennsylvania State University, State College, USA)
15:45 - 16:15 Break
- 15:45 Break 30'
16:15 - 17:30 Lie groupoids and Lie algebroids, VI: integrability and cohomology
- 16:15 Lie groupoids and Lie algebroids, VI: integrability and cohomology 1h15'
  
  Speaker: M. Crainic (Utrecht University, Utrecht, The Netherlands)

Thursday, 14 July 2005

08:45 - 09:45 Quantization of Poisson manifolds, IV
- 08:45 Quantization of Poisson manifolds, IV 1h0'
  
  Speaker: S. Gutt (Université Libre de Bruxelles, Bruxelles, Belgique)
09:45 - 10:00 Break
- 09:45 Break 15'

10:00 - 11:00 Bihamiltonian structures and Frobenius manifolds, IV

10:00 Bihamiltonian structures and Frobenius manifolds, IV 1h0'

Speaker:	B. Dubrovin (SISSA, Trieste, Italy)
Material:	lecture notes

11:00 - 11:20 Break
- 11:00 Break 20'
11:20 - 12:20 Infinite dimensional Poisson geometry and coherent states, IV
- 11:20 Infinite dimensional Poisson geometry and coherent states, IV 1h0'
  
  Speaker: A. Odzijewicz (University of Bialystok, Bialystok, Poland)
12:20 - 14:30 Lunch Break
- 12:20 Lunch Break 2h10'
14:30 - 15:45 Poisson-Lie groups and Poisson groupoids, III
- 14:30 Poisson-Lie groups and Poisson groupoids, III 1h15'
  
  Speaker: P. Xu (The Pennsylvania State University, State College, USA)
15:45 - 16:15 Break
- 15:45 Break 30'
16:15 - 17:30 Lie groupoids and Lie algebroids, VII: integrability and Poisson geometry
- 16:15 Lie groupoids and Lie algebroids, VII: integrability and Poisson geometry 1h15'
  
  Speaker: R. L. Fernandes (Instituto Superior Tecnico, Lisbon, Portugal)

Friday, 15 July 2005
- 08:45 - 09:45 Quantization of Poisson manifolds, V
  - 08:45 Quantization of Poisson manifolds, V 1h0'
    
    Speaker: S. Gutt (Université Libre de Bruxelles, Bruxelles, Belgique)
- 09:45 - 10:00 Break
  - 09:45 Break 15'
- 10:00 - 11:00 Bihamiltonian structures and Frobenius manifolds, V
  - 10:00 Bihamiltonian structures and Frobenius manifolds, V 1h0'
    
    Speaker: B. Dubrovin (SISSA, Trieste, Italy)
- 11:00 - 11:20 Break
  - 11:00 Break 20'
- 11:20 - 12:20 Infinite dimensional Poisson geometry and coherent states, V
  - 11:20 Infinite dimensional Poisson geometry and coherent states, V 1h0'
    
    Speaker: A. Odzijewicz (University of Bialystok, Bialystok, Poland)
- 12:20 - 14:30 Lunch Break
  - 12:20 Lunch Break 2h10'
- 14:30 - 15:45 Poisson-Lie groups and Poisson groupoids, IV
  - 14:30 Poisson-Lie groups and Poisson groupoids, IV 1h15'
    
    Speaker: P. Xu (The Pennsylvania State University, State College, USA)
- 15:45 - 16:15 Break
  - 15:45 Break 30'
- 16:15 - 17:30 Lie groupoids and Lie algebroids, VIII: integrability, foliation theory and homotopy theory
  - 16:15 Lie groupoids and Lie algebroids, VIII: integrability, foliation theory and homotopy theory 1h15'
    
    Speaker: R. L. Fernandes (Instituto Superior Tecnico, Lisbon, Portugal)
Monday, 18 July 2005
- 08:30 - 10:00 REGISTRATION (for new arrivals)
  
  Location: Adriatico Guest House (Lower Level 1)
  - 08:30 REGISTRATION (for new arrivals) 1h30'
- 10:00 - 10:10 OPENING
  - 10:00 OPENING 10'
- 10:10 - 11:05 The notion of moment map for families of symplectomorphisms
  - 10:10 The notion of moment map for families of symplectomorphisms 55'
    
    Speaker: V. Guillemin (Massachusetts Institute of Technology, Cambridge MA, USA)
- 11:05 - 11:30 Break
  - 11:05 Break 25'
- 11:30 - 12:25 Examples of Poisson varieties associated to semi-simple groups
  - 11:30 Examples of Poisson varieties associated to semi-simple groups 55'
    
    Speaker: J.H. Lu (Hong Kong University of Science & Technology, Kowloon, Hong Kong)
- 12:25 - 15:00 Lunch Break
  - 12:25 Lunch Break 2h35'
- 15:00 - 15:55 Ginzburg-Weinstein via Gelfand-Zeitlin
  - 15:00 Ginzburg-Weinstein via Gelfand-Zeitlin 55'
    
    Speaker: A. Alekseev (University of Geneva, Geneva, Switzerland)
- 15:55 - 16:10 Break
  - 15:55 Break 15'
- 16:10 - 17:05 On the Riemann-Poisson manifolds
  - 16:10 On the Riemann-Poisson manifolds 55'
    
    Speaker: A. Boucetta (Université Cady-Ayyad, Marrakech, Morocco)
- 17:05 - 17:30 Break
  - 17:05 Break 25'
- 17:30 - 18:25 Connections of non-abelian differential gerbes
  - 17:30 Connections of non-abelian differential gerbes 55'
    
    Speaker: C. Laurent (Université de Poitiers, Poitiers, France)
Tuesday, 19 July 2005
- 09:00 - 09:55 Automorphisms and derivations of quantum and classical Poisson algebras
  - 09:00 Automorphisms and derivations of quantum and classical Poisson algebras 55'
    
    Speaker: N. Poncin (Université de Luxembourg, Luxembourg)
- 09:55 - 10:10 Break
  - 09:55 Break 15'
- 10:10 - 11:05 to be announced
  - 10:10 to be announced 55'
    
    Speaker: M. Karasev (Technical University (MIEM), Moscow, Russian Federation)
- 11:05 - 11:30 Break
  - 11:05 Break 25'
- 11:30 - 12:25 Deformation quantizations and gerbes
  - 11:30 Deformation quantizations and gerbes 55'
    
    Speaker: Y. Maeda (Keio University, Yokohama, Japan)
- 12:25 - 15:00 Lunch Break
  - 12:25 Lunch Break 2h35'
- 15:00 - 15:55 Modular classes of Lie algebroids
  - 15:00 Modular classes of Lie algebroids 55'
    
    Speaker: Y. Kosmann-Schwarzbach (Ecole Polytechnique, Palaiseau, France)
- 15:55 - 16:10 Break
  - 15:55 Break 15'
- 16:10 - 17:05 Morse theory and algebras of moduli spaces
  - 16:10 Morse theory and algebras of moduli spaces 55'
    
    Speaker: V. Ginzburg (University of California at Santa Cruz, Santa Cruz, USA)
- 17:05 - 17:30 Break
  - 17:05 Break 25'
- 17:30 - 18:25 Quasi-Poisson theory via Dirac geometry
  - 17:30 Quasi-Poisson theory via Dirac geometry 55'
    
    Speaker: H. Bursztyn (I.M.P.A., Rio de Janeiro, Brazil)
Wednesday, 20 July 2005
- 09:00 - 09:55 Poisson structure and quantization of cluster varieties
  - 09:00 Poisson structure and quantization of cluster varieties 55'
    
    Speaker: V. Fock (I.T.E.P., Moscow, Russian Federation)
- 09:55 - 10:10 Break
  - 09:55 Break 15'
- 10:10 - 11:05 Poisson geometry and deformation quantization near a pseudoconvex boundary
  - 10:10 Poisson geometry and deformation quantization near a pseudoconvex boundary 55'
    
    Speaker: A. Weinstein (University of California, Berkeley, USA)
- 11:05 - 11:30 Break
  - 11:05 Break 25'
- 11:30 - 12:25 Ricci-flat symplectic connections
  - 11:30 Ricci-flat symplectic connections 55'
    
    Speaker: S. Gutt (Université Libre de Bruxelles, Bruxelles, Belgique)
- 12:25 - 12:25 FREE AFTERNOON
  - 12:25 FREE AFTERNOON
Thursday, 21 July 2005
- 09:00 - 09:55 On multiplicative 2-forms
  - 09:00 On multiplicative 2-forms 55'
    
    Speaker: M. Crainic (Utrecht University, Utrecht, The Netherlands)
- 09:55 - 10:10 Break
  - 09:55 Break 15'
- 10:10 - 11:05 Poisson structures and bihermitian metrics
  - 10:10 Poisson structures and bihermitian metrics 55'
    
    Speaker: N. Hitchin (University of Oxford, Oxford, UK)
- 11:05 - 11:30 Break
  - 11:05 Break 25'
- 11:30 - 12:25 Noncommutative Kahler-like structures in quatization
  - 11:30 Noncommutative Kahler-like structures in quatization 55'
    
    Speaker: A. Odzijewicz (University of Bialystok, Bialystok, Poland)
- 12:25 - 15:00 Lunch Break
  - 12:25 Lunch Break 2h35'
- 15:00 - 15:55 Some remarks on generalized complex structures
  - 15:00 Some remarks on generalized complex structures 55'
    
    Speaker: P. Xu (The Pennsylvania State University, State College, USA)
- 15:55 - 16:10 Break
  - 15:55 Break 15'
- 16:10 - 17:05 Stability of symplectic leaves
  - 16:10 Stability of symplectic leaves 55'
    
    Speaker: R. L. Fernandes (Instituto Superior Tecnico, Lisbon, Portugal)
- 17:05 - 17:30 Break
  - 17:05 Break 25'
- 17:30 - 18:25 Complete commutative subalgebras in Poisson-Lie algebras: a proof of the Mischenko-Fomenko conjecture
  - 17:30 Complete commutative subalgebras in Poisson-Lie algebras: a proof of the Mischenko-Fomenko conjecture 55'
    
    Speaker: A. Bolsinov (Moscow State University, Moscow, Russian Federation)
Friday, 22 July 2005
- 09:00 - 09:55 On (co-) morphisms of Lie pseudoalgebras and groupoids
  - 09:00 On (co-) morphisms of Lie pseudoalgebras and groupoids 55'
    
    Speaker: Z.J. Liu (Peking University, Beijing, China)
- 09:55 - 10:10 Break
  - 09:55 Break 15'
- 10:10 - 11:05 Reduction for general symplectic actions
  - 10:10 Reduction for general symplectic actions 55'
    
    Speaker: T. Ratiu (E.P.F.L., Lausanne, Switzerland)
- 11:05 - 11:30 Break
  - 11:05 Break 25'
- 11:30 - 12:25 Berezin-Toeplitz quantization of the moduli space of flat SU(N) connections
  - 11:30 Berezin-Toeplitz quantization of the moduli space of flat SU(N) connections 55'
    
    Speaker: M. Schlinchenmaier (Universitat Mannheim, Mannheim, Germany)
- 12:25 - 15:00 Lunch Break
  - 12:25 Lunch Break 2h35'
- 15:00 - 15:55 Symplectic leaf neighborhood theorems
  - 15:00 Symplectic leaf neighborhood theorems 55'
    
    Speaker: Y. Vorobiev (Moscow Inst. of Electronic Tech., Moscow, Russian Federation)
- 15:55 - 16:10 Break
  - 15:55 Break 15'
- 16:10 - 17:05 Dirac structures and the phase space of particles in a Yang-Mills-Higgs field
  - 16:10 Dirac structures and the phase space of particles in a Yang-Mills-Higgs field 55'
    
    Speaker: A. Wade (The Pennsylvania State University, University Park, USA)