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402-0889-90L 6 Credits MSC D-PHYS
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Geometry and Topology in Condensed Matter Physics (University of Zurich)

Lecturers & Examiners: Dr. Tomas Bzdusek
Does not take place this semester. No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: PHY542 Mind the enrolment deadlines at UZH:
VVZ CR n/a

Last Updated: 2026-06-01 11:31:28

Abstract

This course equips the student with an adequate understanding of geometric and topological methods employed in theoretical characterization of classical and quantum matter. Diverse mathematical techniques will be systematically introduced in a semi-formal approach, and the significance of each presented tool will be illustrated through applications to diverse condensed matter systems.

Objective

The objective of the course is to familiarize the student with selected techniques from differential geometry and algebraic topology, and with their applications in the field of condensed matter physics. The course is aimed at the graduate level and requires a basic knowledge of quantum mechanics, solid state physics, and elementary group theory. By the end of this course, the students will understand the relevance of these advanced mathematical tools to diverse physics problems, and they will become familiar with selected topics from recent research of classical and quantum topological matter.

Content

The covered mathematical topics include: homotopy groups, singular homology, Morse theory, Riemannian geometry, vector bundles, parallel transport, characteristic classes, cohomology theory, and Clifford algebras. The applications to condensed matter physics include: defects of order parameters, Van Hove singularities, flat energy bands, topological band theory, gauge fields, tenfold way classification, and topologically ordered phases.

Resources

Lecture Notes

Lecture notes will be provided at the beginning of the semester.The course materials (lectures notes & slides, exercise problems, and solutions sheets) will be diistributed through the Online Learnign and Training (OLAT) platform of the University of Zurich at this link:https://lms.uzh.ch/auth/RepositoryEntry/17577443790

Literature

Suggested complementary literature will be provided in the class.

General Information

Language
English
Levels
MSC
Frequency
Every two years

Examination

Type
graded semester performance
Registration modalities, date and venue of this performance assessment are specified solely by the UZH.

Course Components

Type Title Time & Place Hours
lecture Geometry and Topology in Condensed Matter Physics (University of Zurich)
Does not take place this semester. **Course at University of Zurich** Lectures take place on Fridays 10:15 - 12:00 in Y27-H-35/36.
No time listed 2 h weekly
exercise Geometry and Topology in Condensed Matter Physics (University of Zurich)
Does not take place this semester. **Course at University of Zurich** Exercises start in the second week of the semester and take place on Wednesdays 9:00 - 11:00 in Y36-K-08.
No time listed 2 h weekly

Offered In