Seminar on knot theory

Seminar topic: Knots, links and their invariants

Rima Chatterjee

Summer semester 2024

Every Thursday 10:00-11:30 in Seminar room 2



Knot theory has transformed over the years from a specialized branch of topology to a very popular area of study in mathematics. This theory is particularly appealing because the objects we study here are familiar in the real world. The problems in knot theory arise not only in many branches in mathematics but also in many diverse fields such as biology, chemistry and physics. Although, these problems can be easily stated, it is unclear how one can use mathematical techniques to solve even the basic problems in knot theory.

This semester we plan to explore this fascinating world with a very elementary approach. The goal of this seminar is to introduce knots, links and then discuss how one can distinguish one knot from the other using different type of invariants. Along the way, we also learn about some open problems in this area of mathematics.

Suitable for undergraduate students with some basic knowledge of linear algebra. 

The preliminary discussion meeting will be on 24th January  12-12:30.

Lectures:

11.04.2024      Knots and links, Reidemeister moves [S 1]

                                 Mira J. Wenzel

18.04.2024      The Conway polynomial  [S 2]

                                  Daphne D. Omarova

25.04.2024       The arithmetic of knots  [S 3]

                                  Carla Flesch

02.05.2024        Some simple knot invariants [S 4]

                                  Paula Meessmann

09.05.2024       Holiday

16.05.2024       The Kauffman Bracket [S 5]

                                  Merit Werschy

23.05.2024     Holiday

30.05.2024     Holiday

06.06.2024     The Jones polynomial [S 6]

                               Ole Pgissing

13.06.2024      Braids  [S 7]

                               Daniel Voegele

20.06.2024      Finite type invariants [S 8]

                               Vincent Siebler

27.06.2024      Vassiliev invariants  [S 9]

                                Timo Hauser

04.07.2024      Combinatorial description of Vasilliev invariants [S 10]

                               Benedikt Schoenherr

11.07.2024      The Kontsevich integrals [S 11]

                               Jakob Land





Literature:

[S] A.B. Sossinsky                                           Knots, Links and Their Invariants