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.


Daniel Tubbenhauer email

Please put [Lecture Quantum invariants of links] as the subject.

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