Knot theory seminar, spring 2016

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


The talk on the 22nd of February has been moved to the afternoon of the 24th of February: 15:30-17:30.

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.


Meeting are generally on Monday from 10:00 till 12:00. However, there will be not knot theory seminar on February 22. The meeting in that week will be last one of the seminar and on Wednesday February 24 from 15:30 till 17:30!
118 January405Mima StanojkovskiIntroduction to knots and their fundamental groupsKnotes
225 January405Roland van VeenInvariants of knotsA smooth introduction to knots
31 February405Erik VisseGeometry of knotsKnotes
48 February405Julian LyczakTrace fields of knotsKnotes
515 February405Ted ChinburgKnots, Brauer and Tate-Shafarevich groups
624 February405Alexander PopolitovKnots 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.