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Geometry and Dynamics of Hamiltonian Lie group actions

Course Code :2600WETGDH
Study domain:Mathematics
Academic year:2019-2020
Semester:2nd semester
Contact hours:30
Study load (hours):84
Contract restrictions: No contract restriction
Language of instruction:English
Exam period:exam in the 2nd semester
Lecturer(s)Marine Fontaine

3. Course contents *

  • Background on Lie groups and Lie algebras, symplectic manifolds and hamiltonian Lie group actions.
  • Definition and examples of Hamilonian G-manifolds.
  • Definition and examples of momentum maps with their geometric properties.
  • Schur-Horn theorem in linear algebra and moment polytopes.
  • Basics of Morse-Bott theory with application to hamiltonian torus actions.
  • The Atiyah-Guillemin-Sternberg convexity theorem.