Masterclass on Topological quantum field theories, quantum groups and 3-manifold invariants – University of Copenhagen

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Masterclass on Topological quantum field theories, quantum groups and 3-manifold invariants 

The University of Copenhagen

October 6-10, 2014

The main part of the program of the masterclass consisted of the following lecture series by Chris Douglas and Andre Henriques

Title: Quantum groups and 3-manifold invariants

Abstract: "The aim of this meeting is to introduce the theory of quantum groups and their representations, and to investigate associated 3-dimensional topological quantum field theories (TQFTs). We will investigate the braided tensor structure of the representation category of a quantum group and the modularity property of the semisimple quotient, when the quantum parameter q is a root of unity. We will then discuss the Reshetikhin-Turaev construction of a 3-dimensional TQFT from a modular category. Finally, we will describe the modern, higher-categorical perspective on TQFTs that includes not only invariants of 2- and 3-manifolds but also algebraic data associated to manifolds of every codimension."

In addition, there will be a series of lectures titled 'From subfactors to invariants of 3-manifolds' by Ryszard Nest, supported by two introductory lectures by Hiroshi Ando.

Schedule: Registration is on Monday, 8:45 - 9:15 in front of Auditorium 6.

DH = Christopher Douglas & André Henriques - Quantum groups and 3-manifold invariants
HA = Hiroshi Ando - Introductory lectures on  the hyperfinite II_1 factor and standard form
RN = Ryszard Nest - From subfactors to invariants of 3-manifolds
CC = Clarisson Rizzie Canlubo - What is a quantum group? (seminar talk)

Monday Tuesday Wednesday Thursday Friday
8:45-9:15 Registration
Lecture 1 9:15-10:00

Aud 6

Chris 1

Zoo A Chris 3

Aud 8 Chris 5

Aud 3


Aud 4 Ryszard3
Coffee/fruit 10:00-10:30
Lecture 2 10:30-11:15

Aud 6

Hiroshi 1

Zoo A Chris 4

Aud 8

Hiroshi 2

Aud 3 August Kroh


Aud 2 Ryszard4
Break 11:15-11:25
Lecture 3 11:25-12:10

Aud 6

Chris 2

Zoo A

Andre 3

Aud 8

Andre 5

Aud 3 August Krogh

Chris 6

Aud 2 Andre 8
Lunch 12:10-14:00
Lecture 4 14:00-14:45 Bio 4.0.24 Andre 1 Aud 1 Andre 4

Aud 2

Andre 6

Aud 2 Chris 7 Aud 10 Chris 8
Coffee/cake 14:45-15:15
Lecture 5 15:15-16:00 Bio 4.0.24 Andre 2 Aud 1 Clarisson

Aud 2


Aud 2 Andre 7 Aud10 Q&A
16:00-17:00 Q&A Q&A Q&A
Pizza & Beer

Additional material: Schommer-Pries, The Classification of Two-Dimensional Extended Topological Field Theories.  Hiroshi Ando's own Notes with proofs and some extras. Video's of an earlier incarnation of Douglas and Henriques' series. New typed versions of Andre's handouts: handout 1, handout 2, handout 3.

Venue: Centre for Symmetry and Deformation, KU. For information how to get to the Department of Mathematical Sciences click here

Registration: Registrations have closed on September 26.

Accommodation: We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. The small Hotel Rye is also a good local option. Other inexpensive alternatives are CabInn that has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandivania (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Somewhat more expensive - and still recommended - options are Hotel Nora and Ibsen's Hotel

Funding: Participants can apply for financial support to partly cover local expenses.  If you wish to apply for support, please indicate this on the registration form. The support will be DKK 500 per day, at most DKK 2500. 

This masterclass is supported by the PhD-school of the Faculty of SCIENCE, Copenhagen University and the Centre for Symmetry and Deformation.


Massimiliano Ungheretti and Nathalie Wahl