This is the web page for the knot theory seminar 2016 run by Mima Stanojkovski and Julian Lyczak.

After the talk we will go out for dinner at the pancake house near the station. Please sign up with the organizers if you want to join.

Knots are fascinating mathematical objects with relations to topology, geometry and number theory. In this seminar we will demonstrate some of these connections.

# | Date | Room | Speaker | Subject | Knotes |
---|---|---|---|---|---|

1 | 18 January | 405 | Mima Stanojkovski | Introduction to knots and their fundamental groups | Knotes |

2 | 25 January | 405 | Roland van Veen | Invariants of knots | A smooth introduction to knots |

3 | 1 February | 405 | Erik Visse | Geometry of knots | Knotes |

4 | 8 February | 405 | Julian Lyczak | Trace fields of knots | Knotes |

5 | 15 February | 405 | Ted Chinburg | Knots, Brauer and Tate-Shafarevich groups | |

6 | 24 February | 405 | Alexander Popolitov | Knots and physics |

- The Knot atlas contains a lot of information on knots. For example, here is a list of all knot with at most 10 crossings.
- This webpage allows you to show all knots with specific properties up to 12 crossings.
- The free program SnapPy allows one to draw knots and compute invariants.
- More software on knots can be found here.
- A video (or an alternative link) on the hyperbolic structure of the complement of the Borromean rings.
- An article on the first 1.7 million knots.
- A well written master thesis on knots.
- The course knotes Knots and primes by Chao Li and Charmaine Sia on the relation between knots and primes.
- A complete lecture course by Dror Bar-Natan. The course focusses on the relation between knots and Lie algebras.
- A video of the talk Azumaya algebras associated to knot groups by Ted Chinburg. His talk in our seminar will be of similar content.

[Adams] | Colin Adams: is an easygoing and well written popular account including everything from open problems to knot-jokes.The Knot Book |

[Burde-Zieschang] | Burde & Zieschang: .Knots is a solid exposition |

[CCGLS] | Cooper, Culler, Gillet, Long & Shalen: is a fundamental paper. You can get it here.Plane curves associated to character varieties of 3-manifolds |

[Fox] | R.H. Fox: A Quick Trip Through Knot Theory |

[Gelca] | Razvan Gelca: . This recent book using some physics/representation theory to explain why theta functions are knotted.Theta functions and knots |

[Hikami-Lovejoy] | Hikami & Lovejoy: . This paper relates knots and quantum modular forms.Torus knots and quantum modular forms |

[Kohno] | Kohno: . Kohno wrote a beautiful account of the connection between conformal field theory and knot theory.Conformal field theory and topology |

[Likorish] | W.B. Raymond Likorish: is sometimes referred to as the new testament of knot theory. A solid graduate text.An introduction to knot theory |

[McLachlan-Reid] | McLachlan & Reid: . Since most knots can be described as hyperbolic manifolds one may ask how topological properties of the knot interact with arithmetic properties of the corresponding discrete subgroup of \(\rm{SL}(2,C)\).Arithmetic of hyperbolic 3-manifolds |

[Morishita] | Morishita: introduces both algebraic number theory (primes) and low dimensional topology (knots), emphasizing the analogies between the subjects.Knots and primes |

[Murasagi] | Kunio Murasagi: are relatively short but clear notes on more knot invariants then we will cover in this seminar. They are available here.Classical Knot Invariants and Elementary Number theory |

[Ohtsuki] | Tomotada Ohtsuki: is a good introduction to quantum invariants in knot theory.Quantum invariant: a study of knots, 3-manifolds and their sets |

[Rolfsen] | Rolfsen: is sometimes called the old testatment of knot theory.Knots and links |