Schriftzug: Fachbereich Mathematik 
  UHH > Fakultäten > MIN-Fakultät > Mathematik > Personen   Sitemap Suchen Hilfe there is no english version of this page  

65-502: Algebra Seminar - Quantum invariants (Summer term 2015)


Ralf Holtkamp and Louis-Hadrien Robert

Time and place:

On Thursday at 10:30 in Room 1240 (Geomatikum).


In this seminar we will define and study quantum invariants of knots and 3-manifolds. We will begin by a few talks about semi-simple Lie algebras and their representations. The planned talks are:

  • 1 Introduction and overview. 02.04.2015 (LHR)

  • 2 Lie Algebras, semi-simplicity, Killing's form. Following [H, §1, § 2.(4-6)]. 09.04.2015 (SM)

  • 3 Representation of sl(2,C), roots, root systems. Following [H, § 2.(7-8), §3.9]. 16.04.2015 (LW)

  • 4 Representations of sl(n, C) Following. [FH, §15].

  • 5 Definition of the Uq(sl(n,C)) and first properties. Following [KRT, §:4].

  • 6-7 Invariant of tangles, links and 3-manifolds. Following [KRT, §5-6] and [O, §8].

  • 8 Representation of Uq(sl(n),C). Following [KRT, §7].

  • 9 Vassiliev invariants. Following [KRT, §8]. June 2015 (EE)

  • 10/11 Categorification of the Jones polynomial. Following [BN].


 [BN] D. Bar-Natan, On Khovanov's Categorification of the Jones Polynomial, Algebraic and Geometric Topology, MSP.

 [FH] W. Fulton and J. Harris, Representation Theory. A first course, Springer.

 [KRT] C. Kassel, M. Rosso and V. Tuarev, Quantum groups and knot invariants, SMF.

 [H] J. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer

 [O] T. Ohtsuki, Quantum Invariants, World Scientific.


The seminar is aimed at Master students in mathematics or mathematical physics, but is also open for Bachelor students who are familiar with the contents of an Algebra I course.


Depending on the interest of the participants, we may treat the following additional subjects:

  • Rasmussen invariant,
  • Kirby moves,
  • Homfly-pt polynomial.

First Meeting:

A first meeting took place on Thursday 05/02/2015. If you are interested, but you did not attend this meeting, please send an email to (replace the names by some adequate values).

  zurück Seitenanfang  Impressum <