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401-4816-DRL 1 Credits DR D-MATH

Geometric Methods in Mathematical Physics

Lecturers & Examiners: Dr. Michele Schiavina
Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.
VVZ CR n/a

Last Updated: 2026-02-05 16:07:26

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
DR

Examination

Type
ungraded semester performance
The exam is only offered in the Summer 2022 Examination Session. In particular, a repetition exam cannot be offered.

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Geometric Methods in Mathematical Physics
  • Mon 16:15-18:00 (HG E 22)
  • 31.05 Date 09:15-11:00 (HG E 22)
2 h weekly

Offered In

  • Doctorate Mathematics (More Information at: )
    • Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
      • Graduate School (Official website of the Zurich Graduate School in Mathematics: In addition to the 401-....-DRL course units, adapted versions for doctoral students of the following course units: 263-4400-00L Advanced Graph Algorithms and Optimization 401-3902-21L Network & Integer Optimization: From Theory to Application 401-3904-22L Convex Optimization 401-3629-00L Quantitative Risk Management 401-3652-00L Numerical Methods for Hyperbolic Partial Differential Equations 151-0530-00L Nonlinear Dynamics and Chaos II 227-0434-10L Mathematics of Information 401-4490-22L Topology Optimization of Engineering Systems ... (continued ))