This is the web page for the knot theory seminar 2016 run by Mima Stanojkovski and Julian Lyczak.
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 |
| [Adams] | Colin Adams: The Knot Book is an easygoing and well written popular account including everything from open problems to knot-jokes. |
| [Burde-Zieschang] | Burde & Zieschang: Knots is a solid exposition. |
| [CCGLS] | Cooper, Culler, Gillet, Long & Shalen: Plane curves associated to character varieties of 3-manifolds is a fundamental paper. You can get it here. |
| [Fox] | R.H. Fox: A Quick Trip Through Knot Theory |
| [Gelca] | Razvan Gelca: Theta functions and knots. This recent book using some physics/representation theory to explain why theta functions are knotted. |
| [Hikami-Lovejoy] | Hikami & Lovejoy: Torus knots and quantum modular forms. This paper relates knots and quantum modular forms. |
| [Kohno] | Kohno: Conformal field theory and topology. Kohno wrote a beautiful account of the connection between conformal field theory and knot theory. |
| [Likorish] | W.B. Raymond Likorish: An introduction to knot theory is sometimes referred to as the new testament of knot theory. A solid graduate text. |
| [McLachlan-Reid] | McLachlan & Reid: Arithmetic of hyperbolic 3-manifolds. 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 \(\rm{SL}(2,C)\). |
| [Morishita] | Morishita: Knots and primes introduces both algebraic number theory (primes) and low dimensional topology (knots), emphasizing the analogies between the subjects. |
| [Murasagi] | Kunio Murasagi: Classical Knot Invariants and Elementary Number theory are relatively short but clear notes on more knot invariants then we will cover in this seminar. They are available here. |
| [Ohtsuki] | Tomotada Ohtsuki: Quantum invariant: a study of knots, 3-manifolds and their sets is a good introduction to quantum invariants in knot theory. |
| [Rolfsen] | Rolfsen: Knots and links is sometimes called the old testatment of knot theory. |