Course Code : | 2600WETGDH |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

Semester: | 2nd semester |

Contact hours: | 30 |

Credits: | 3 |

Study load (hours): | 84 |

Contract restrictions: | No contract restriction |

Language of instruction: | English |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Marine Fontaine |

At the start of this course the student should have acquired the following competences:

an active knowledge of

an active knowledge of

- English

- English

- The student will acquire some knowledge on Lie groups and their representations, Lie algebras, symplectic manifolds equipped with a hamiltonian Lie group action, momentum maps, and some knowledge on Morse-Bott theory. Those tools are applied to prove the convexity theorem of Atiyah-Guillemin-Sternberg in symplectic geometry. This theorem generalises the well-known Schur-Horn theorem in linear algebra whose connection to symplectic geometry is not evident a priori.

- 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.

Class contact teachingLectures Practice sessions

Personal workExercises Assignments Individually

Personal work

Continuous assessmentAssignments

The lecture is given on the blackboard and more detailed lecture notes will be provided after each session.

Book references will be provided in due time on the course website.

marine.fontaine@uantwerpen.be