“Lecture Quantum invariants of links”
Quantum invariants are more than just topological invariants needed to tell objects apart.
They build bridges between topology, algebra, number theory and quantum physics helping to transfer ideas,
and stimulating mutual development. They also have a deep and interesting connection to representation theory, in particular, to representations of quantum groups.
In this course we will introduce these objects from different perspectives: skein and representation theoretic.
We will start with the Jones polynomial, study its properties, and then move to the categorification of this polynomial
discovered by Khovanov. In the second part (i.e. this lecture) of the class we will explain its connections to representation theory following the ideas of e.g.
Reshetikhin-Turaev, and then explain how the categorification also arises from very natural constructions in categorical representation theory.
Contact
Daniel Tubbenhauer email
Please put [Lecture Quantum invariants of links] as the subject.
Who?
-
MSC or PhD students in Mathematics interested in a mixture of (linear) algebra, topology
and category theory, but everyone is welcome.
Where and when?
- Usual session:
- Every Monday from 10:15-12:00
- Online, videos will be posted at Click
- First lecture: 01.Feb.2021
- Last lecture: 05.Apr.2021
- Lecture notes can be found here: Click, which will be updated regularly.
- Please read the notes carefully.
- Asking question via email is of course also allowed.
- Summary:
- Mini presentation:
Schedule
- 01.Feb.2021, Speaker: Daniel Tubbenhauer, Topic: Categories - definitions, examples and graphical calculus
- 08.Feb.2021, Speaker: Daniel Tubbenhauer, Topic: Monoidal categories I - definitions, examples and graphical calculus
- 15.Feb.2021, Speaker: Daniel Tubbenhauer, Topic: Monoidal categories II - more graphical calculus
- 22.Feb.2021, Speaker: Daniel Tubbenhauer, Topic: Pivotal categories - definitions, examples and graphical calculus
- 01.Mar.2021, Speaker: Daniel Tubbenhauer, Topic: Braided categories - definitions, examples and graphical calculus
- 08.Mar.2021, Speaker: Daniel Tubbenhauer, Topic: Additive, linear and abelian categories I - definitions and examples
- 15.Mar.2021, Speaker: Daniel Tubbenhauer, Topic: Additive, linear and abelian categories II - enrich the concepts from before
- 22.Mar.2021, Speaker: Daniel Tubbenhauer, Topic: Fusion and modular categories I - definitions and graphical calculus
- 29.Mar.2021, Speaker: Daniel Tubbenhauer, Topic: Fusion and modular categories II - modularity
- 05.Apr.2021, Speaker: Daniel Tubbenhauer, Topic: Quantum invariants - finally
Goals of the talks
Here is the detailed plan. Click