Talks and slides

Here you'll find a list of talks I have given during my years as a PhD student, and the slides or notes that accompanied them.

  • Concordance orders of knots, Scottish Topology Seminar, 1st July 2010. I explain the main result of my thesis and the open questions still to be answered.
  • Torus knot signatures. Glasgow Geometry and Topology seminar, 30th November 2009. I prove a formula for a special kind of signature of torus knots and explain the uses for it in the theory of slice knots and concordance.
  • Knots and Braids: An introduction. Maths in Astronomy, 24th September 2009. This talk is an introduction to the ideas and techniques from knot theory, designed for a 15 minute talk given to non-mathematicians. (Warning: 6Mb)
  • Slice Knots: Knot Theory in the 4th Dimension. The Mathematics of Knots: Theory and Application, 9th December 2008. A lengthier version of my LMS talk in which I tried to give an introduction to the theory of slice knots and some of the open questions in the subject.
  • Slice Knots: Knot Theory in the 4th Dimension. LMS Graduate Student Conference, 4th July 2008. In this short talk I give the definition of a slice knot, some geometrical intuition and some algebraic invariants to detect sliceness. I then introduce the open question of finding torsion among slice knots.
  • Pirates of the Cobordism: Curse of the Knot Surgery. Geometry Club, 2nd May 2008. This talk explains the definition of the oriented cobordism groups, and proves that in dimensions 1,2 and 3 they are all zero. The main result is that every 3-manifold is the boundary of a 4-manifold, which is proved using surgery on knots.
  • Braids and their applications. PG Colloquium, 26th October 2007. I discussed the latest applications of braids to Physics, Cryptography, Robotics and Quantum Computing. (Warning: 8Mb file!)
  • An algorithm to compute Seifert matrices from braids. Scottish Topology seminar, 6th September 2007. A slightly more detailed version of my Singapore talk.
  • An algorithm to compute Seifert matrices from braids. Singapore Program on Braids, June 2007.
  • The Alexander Polynomial. Geometry Club, 25th May 2007. Its history, how to compute it, why we like it and why it's not always good enough.
  • DNA or knot DNA? That is the question. PG Colloquium, 1st February 2007. This talk looked at the role that knot theory plays in analysing how enzymes act on DNA.