Universität Wien

250119 VO Spinors and Dirac Operators (2023W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
ON-SITE
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 02.10. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.10. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.10. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.10. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.10. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.11. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.11. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.11. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.11. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.12. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.12. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.01. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.01. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 18.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.01. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.01. 15:00 - 16:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Lecture course on the basics of Spin geometry and Dirac operators. We will start with the case of low dimensions, where the spin groups can be described in terms of classical Lie groups and basic Dirac operators can be constructed by hand. Then we will move to general dimensions, discussing the general concept of spin structures and Dirac operators and their relation to Riemannian geometry. The question of existence and uniqueness of Spin structures gives rise to connections to algebraic topology and characteristic classes. Finally we will discuss the general construction of Spin groups via Clifford algebras and hint on the role of Dirac operators in index theory.

The main background required for the course is analysis on manifolds and the basics of differential geometry and Lie group theory. Background on Riemannian geometry, deeper aspects of Lie theory and algebraic topology can be helpful but is not required.

Assessment and permitted materials

Oral exam after the end of the course, no materials permitted.

Minimum requirements and assessment criteria

The usual standards for oral exams on topics courses in the master program are applied.

Examination topics

The contents of the course.

Reading list

Lecture notes which also contain references to further literature will be available via http://www.mat.univie.ac.at/~cap/lectnotes.html . The version from 2017 that is currently online on that page will be reworked a bit before the beginning of the course.

Association in the course directory

MGEV

Last modified: Th 18.07.2024 07:06