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Ingo Runkel
Master Seminar: Hopf algebras, tensor categories and three-manifold invariants - Summer term 2020
Announcements:
- [30.9] The seminar will take place in block form and online, see below for the time table.
Program:
On each day there will be two talks, the schedule for each day is
- 9:00-10:00 talk 1
- 10:00-10:20 discussion
- short break
- 10:30-11:30 talk 2
- 11:30-11:50 discussion
The distribution of talks is as follows:
List of talks:
A short description of the individual talks can be found here: [PDF]
Topic:
In this seminar we will study relations between certain algebraic objects and three-dimensional topology. On the algebraic side, the main ingredients will be Hopf algebras with extra structure, such as an R-matrix, and tensor categories equipped with braiding isomorphisms. On the topological side, we will study invariants of knots and links, invariants of three-manifolds, as well as three-dimensional topological field theories. We will meet, amongst other things, the Jones polynomial, the Hennings invariant, Surgery invariants, the Reshetikhin-Turaev construction, and the universal construction of a topological field theory form a manifold invariant. The focus of this seminar is algebraic, results from topology, such as Reidemeister moves or surgery presentations, will be reviewed but are otherwise taken as given.
This seminar is primarily intended for Masters students in Mathematics and Mathematical Physics. Some knowledge of Hopf algebras and their categories of representations is helpful, but will also be reviewed in the first few talks. This seminar will be held in English.
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