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Topological Quantum Field Theory

CIT413061Elective Modules6 ECTSEnglishUnregelmäßigDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You will learn the formal description of topological quantum field theories as functorial objects, with a focus on two-dimensional theories. In the end you can apply the fundamental definitions and examples, understand proofs, and perform simple calculations for 2D TQFTs.

What you will be able to do

  • Understanding the definition of TQFTs as functors (Atiyah/Segal)
  • Knowledge of typical examples such as finite gauge theories and state-sum models
  • Application of Morse theory for classification in 2D
  • Understanding of defects, boundary theories and their interpretation as symmetries
  • Insight into extended 2D-TQFTs
  • Ability to follow proofs of the treated results and to reproduce proof ideas

What the module consists of

  • LectureConveying theory, definitions and proofs
  • ExerciseDiscussion of problem sheets for deepening understanding and computation of examples

Teaching method

  • In-person lectureIntroduction of concepts, proof techniques and theoretical presentation
  • Tutorial groups with problem sheetsApplication of methods to exercises and discussion of concrete examples
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