“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.
ReshetikhinTuraev, 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 10:1512:00
 Online, prerecorded 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.
 Lecture notes with scribbles (from the videos) 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  definitions and examples
 15.Mar.2021, Speaker: Daniel Tubbenhauer, Topic: Fiat and tensor categories  enrich the concepts from before
 22.Mar.2021, Speaker: Daniel Tubbenhauer, Topic: Fiat, tensor and fusion categories  definitions and classifications
 29.Mar.2021, Speaker: Daniel Tubbenhauer, Topic: Fusion and modular categories  definitions and graphical calculus
 05.Apr.2021, Speaker: Daniel Tubbenhauer, Topic: Quantum invariants  a diagrammatic approach
Goals of the talks
Here is the detailed plan. Click