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.
Reshetikhin-Turaev, 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? (New plan)
- Due to the Corona outbreak, all talks are canceled and we will do an online reading seminar instead. The original schedule can be
found below.
- Lecture notes can be found here: Click, which will be updated regularly.
- Please read the notes carefully.
- There is a discussion group in OLAT where you can ask questions or report errors or typos in the lecture notes.
- Asking question via email is of course also allowed.
Where and when? (Original plan - not valid anymore)
- Usual session:
- Every Monday from 10:15-12:00
- Room Y27H25, University Zurich, Institute of Mathematics
- First lecture: 02.Mar.2020
- Last lecture: 25.May.2020
- Exceptions:
- The lecture from Monday the 02.Mar.2020 was canceled and will take place on 09.Mar.2020 at the usual time 10:15-12:00.
- The lecture from Monday the 09.Mar.2020 is moved to 10.Mar.2020, 10:15-12:00, room Y27H28.
- Summary:
- Mini presentation:
Schedule (Original plan - not valid anymore)
- 09.Mar.2020, Speaker: Daniel Tubbenhauer, Topic: Categories - definitions, examples and graphical calculus, Click
- 10.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 (Time and dates are not valid anymore)
Here is the detailed plan. Click