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