MAT755: “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. (This is the topic of the block course.) 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.
Note that there is a block course given by Anna Beliakova. You have to sign in for this course if you want to get credits.
However, the material covered by the block course and by this lecture are independent of one another and it is no problem
to follow only the block course or the lecture.
Contact
Daniel Tubbenhauer email
Please put [Lecture Quantum invariants of links] as the subject.
Online System of the UZH
This website is up to date, and not the ones from the UZH.
However, please still register yourself online.
See also:
Click,
Click
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
 Room Y27H25, University Zurich, Institute of Mathematics
 First lecture: 02.Mar.2020
 Last lecture: 25.May.2020
 Summary:
 Mini presentation:
Schedule
 02.Mar.2020, Speaker: Daniel Tubbenhauer, Topic: Categories  definitions, examples and graphical calculus, Click
 09.Mar.2020, Speaker: Daniel Tubbenhauer, Topic: Monoidal categories I  definitions, examples and graphical calculus, Click
 16.Mar.2020, Speaker: Daniel Tubbenhauer, Topic: Monoidal categories II  more graphical calculus, Click
 23.Mar.2020, Speaker: Daniel Tubbenhauer, Topic: Pivotal categories  definitions, examples and graphical calculus, Click
 30.Mar.2020, Speaker: Daniel Tubbenhauer, Topic: Braided categories  definitions, examples and graphical calculus, Click
 06.Apr.2020, Speaker: Daniel Tubbenhauer, Topic: Additive, linear and abelian categories I  definitions and examples, Click
 27.Apr.2020, Speaker: Daniel Tubbenhauer, Topic: Additive, linear and abelian categories II  enrich the concepts from before, Click
 04.May.2020, Speaker: Daniel Tubbenhauer, Topic: Fusion and modular categories I  definitions and graphical calculus, Click
 11.May.2020, Speaker: Daniel Tubbenhauer, Topic: Fusion and modular categories II  modularity, Click
 18.May.2020, Speaker: Daniel Tubbenhauer, Topic: Quantum invariants  finally, Click
Goals of the talks
Here is the detailed plan. Click