Mathematics and Physics in Heidelberg Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik Mathematisches Institut Karl-Theodor-Brücke Surprise Fakultät für Physik und Astronomie Fakultät für Physik und Astronomie Institut für Theoretische Physik Universität Heidelberg Universität Heidelberg Universität Heidelberg

Seminar in the Summer Term 2017

Physical Applications of Topological Quantum Field Theory


News

We still have several open slots. If you are interested in giving a talk, please come to the organizational meeting on April 19 (4pm, SR Statistik).

Meeting time and place: Wednesday 16h s.t., MATHEMATIKON SR Statistik 2/104
First talk on April 26.

Instructors

Dr. Richard Eager, eager@mathi.uni-heidelberg.de
Dr. Ingmar Saberi, saberi@mathi.uni-heidelberg.de
Prof. J. Walcher, walcher@uni-heidelberg.de

Description

A quantum field theory is called topological if the correlation functions of its local fields are independent of any background metric, and thereby only sensitive to the underlying topology. TQFTs can be approached axiomatically or given concrete path-integral representations, and have found numerous applications in pure mathematics for the flexible manipulation of various topological invariants, exempli gratia in knot theory.
In the seminar this summer, we will explore some of the applications that topological quantum field theories have found in describing nature, especially in low-dimensional condensed matter physics and in cosmology. Unifying themes will be quasi-particle excitations which obey fractional or non-abelian braid statistics, and the interplay between bulk and edge degrees of freedom through anomalies.
Participants of the seminar will acquire the physical and mathematical background needed to understand modern applications of TQFT, which constitute several exciting and actively developing fields of current research.

Prerequisites: The seminar is aimed at Masters students and advanced Bachelor students of mathematics and physics, and is accessible with a modest amount of background in quantum field theory and basic notions of algebraic topology and representation theory.


Schedule of Talks

Schedule still subject to change.

Date Speaker TitleAbstractNotes
April 26 Fabio 2D TQFT and Frobenius manifolds
May 3 Alejandro Variation of Morse theory
May 10 Hyukjin Cobordism hypothesis
May 17 Georg Berry Phase
May 24 Tobias Integer and Fractional Quantum Hall effect
May 31 Roman Laughlin wave-function
June 7 Menelaos Anyons
June 28 Ade Intro to Chern-Simons
July 5 Robert Knot invariants
July 12 Lukas Quantum computing