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Geometric Methods in Mathematical Physics
Last Updated: 2026-02-05 16:06:47
Abstract
The course will cover selected topics in mathematical physics, focusing on their geometric underpinning. The main common denominator will be the notion of quantisation and the course material will range through several techniques to make sense of it from a mathematical standpoint.
Objective
The objective of this course is to expose master and graduate students in mathematics and physics to a number of successful geometric techniques in mathematical physics. The course will provide a foundation to essential topics in symplectic and Poisson geometry and its application to fundamental questions in classical and quantum physics. It is aimed at mathematics/physics masters and graduate students with an interest but no previous background in symplectic geometry, and students who want to focus on more formal aspects of classical and quantum physics.
Content
In progress: Basics of Symplectic and Poisson geometry. Geometric structure of coadjoint orbits. Hamiltonian group actions, equivariant momentum maps and symplectic reduction. Elements of geometric and deformation quantisation.
Resources
Literature
S. Bates and A. Weinstein, Lectures on the geometry of Quantisation, Berkeley Mathematics Lecture notes, Volume 8, AMS. A. Weinstein, Lectures on Symplectic manifolds, Regional Conference Series in mathematics, Number 29, CBMS, AMS. J-P. Ortega and T. Ratiu, Momentum Maps and Hamiltonian Reduction, Progress in Mathematics, volume 222, Springer To be completed
General Information
- Language
- English
- Levels
- MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Geometric Methods in Mathematical Physics |
|
2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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