University of Durham --- Department of Mathematical Sciences


Topology Reading Group

Each term we choose a topic and hold a weekly informal seminar. Faculty, graduate students, and some undergraduates attend. For further information contact the organizers Andrew Lobb or Dirk Schuetz.

2015/2016 - Chern-Simons-Witten and beyond.


We shall be trying to understand how the Jones polynomial and related invariants arise from the Chern-Simons functional.
We meet Friday afternoons in my office CM102 at 1:30pm. Prior to meeting we have Topology Tea in the common room at 1pm - biscuits are served.

2015-2016 Chern-Simons-Witten and beyond

This is being maintained now by Patrick Orson at this website.

Past topics


2014/2015 - low dimensional topology.

November 21st Andrew Lobb First meeting: Khovanov-Floer theories and that.
November 28st Andrew Lobb All nice Khovanov-Floer theories are functorial.
December 5th Andrew Lobb The Sato-Levine invariant.
December 12th Andrew Lobb The Sato-Levine invariant and the Pontryagin class.
January 16th Will Rushworth The slice genus of torus knots: what has it ever done for us?...
January 23rd Will Rushworth The slice genus of torus knots: what has it ever done for us?...
January 30th Patrick Orson High-dimensional slice knots.
February 6th. No speaker. Chilling.
February 13th Patrick Orson High-dimensional slice knots continued.
February 20th. Andrew Lobb. Something about 3-manifolds.
March-May Various Curvature and connections in principal bundles.

Epiphany 2014 Lectures

January 31st Dan Jones Floer differential
February 7th Jonathan Grant Singular knots and Floer homology.
We had much more but we forgot to record it!.

Michaelmas 2013 - melange de la topologie.

Michaelmas 2013 Lectures

October 9th Jonathan Grant and Dan Jones Heegaard-Floer and Lattice cohomology.
October 16th Mauro Mauricio, Renyi Institute. Left orderability.
October 30th John Hunton Nine views of a pattern space, continued...
November 6th Lukas Lewark The Khovanov-Rozansky concordance invariants.
November 13th Andrew Lobb Sort-of universality of Khovanov homology, maybe.
November 20th Dirk Schuetz Intersection homology for linkage spaces in odd dimensional Euclidean space.
November 27th Vitaliy Kurlin Introduction to Topological Data Analysis.

In Michaelmas and Epiphany terms 2012-2013 we studied hyperbolic 3-manifolds, looking in particular at hyperbolic structures on knot complements and on 3-manifolds resulting from knot surgery. . Much of the work in the subject was done by William Thurston, and culminated in his famous Geometrization Conjecture, the relatively recent proof of which included the Poincare Conjecture as a corollary. Thurston's notes on the subject are available as a free pdf. For an expanded version of the earlier chapters there is the book by Thurston and Levy

Epiphany 2013 Lectures

January 17th All Organizational meeting
January 24th Pavel Tumarkin Completeness and ideal polyhedra
January 31st Ramon Vera The Dehn surgery invariant
February 7th Dan Jones Dehn surgery on the Figure 8 knot
February 14th Vitaliy Kurlin A description of closed 3-manifolds that allow hyperbolic foliations
February 21st John Parker More on hyperbolic foliations
February 28th Andrew Lobb The Figure 8 knot is fibred. Here's the monodromy calculation
March 7th Dirk Schuetz Incompressible surfaces in a certain knot complement.

Michaelmas 2012 Lectures

October 11th Andrew Lobb Visualizing the Figure 8 complement
October 18th John McLeod Distances and angles in hyperbolic space
October 25th All speakers. Organizational meeting.
November 1st Dirk Schuetz Geometric structures and link complements
November 8th Jonathan Grant Developing map and horospheres
November 15th Luke Stanbra Ideal polyhedra and gluing, dimension 2.
November 22nd Dan Jones Ideal tetrahedra and gluing, dimension 3.
November 29th Marjan Safi-Samghabadi Hyperbolic structure on the Figure Eight knot.
December 6th John Parker A discussion based on the video "Not Knot".

Materials

Photos from the first lecture: visualizing the Figure 8 complement. 1, 2, 3, 4.


Khovanov homology and homotopy types, Epiphany and Easter terms 2012.