
65502: Algebra Seminar  Quantum invariants (Summer term 2015)
Veranstalter: 
Ralf Holtkamp
and
LouisHadrien Robert

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

Description:

In this seminar we will define and study quantum invariants of knots and 3manifolds. We will begin by a few talks about semisimple Lie algebras and their representations. The planned talks are:
1 Introduction and overview.
02.04.2015 (LHR)
2 Lie Algebras, semisimplicity, Killing's form.
Following
[H, §1, § 2.(46)]. 09.04.2015 (SM)
3 Representation of sl(2,C), roots, root systems.
Following
[H, § 2.(78), §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].
67 Invariant of tangles, links and 3manifolds.
Following
[KRT, §56] 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].

Literature:

[BN] D. BarNatan, 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.

Prerequisites:

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.

Remarks:

Depending on the interest of the participants, we may treat the following additional subjects:
 Rasmussen invariant,
 Kirby moves,
 Homflypt 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 firstname.lastname@unihamburg.de (replace the names by some adequate values).


