Talks: slides and videos

Non-commutativity and the Dirac operator

Odense May 2019 This is an introductory talk explaining how the Dirac operator in high-energy physics has the structure of a non-commutative geometry, and how I hope to use this structure to construct models of quantum gravity.

Nottingham 2017 Another talk with a similar aim. It starts with a discussion of the Planck scale and non-commutativity and ends with a brief description of the first paper with Lisa Glaser on random non-commutative geometries.

The talk in Nijmegen in April 2016 at the conference on Gauge Theory and Noncommutative Geometry explains how the axioms of non-commutative geometry can be written in as geometric moves on diagrams (in the same way as moves on spin networks express the relations in a spherical category). The talk starts with an informal explanation of how these relate to Feynman diagrams for Dirac particles.

The spin foam lectures

Jan 2013 UNAM Mexico version:

• Lecture 1: Introductory and spin networks.  Slides
• Lecture 2: State sum models. Slides
• Lecture 3: 3d spin foam models. Slides
• Lecture 4: 4d spin foam models. Slides

The first lecture is the same as Caen (minor corrections) but the remaining ones are new.

September 2010, Caen version:

• Lecture 1: Spin networks. Slides
• Lecture 1b: Spherical categories. Slides and screencast mp4
• Lecture 2: Skein algebra. Slides and screencast of part 1 mp4, and part 2 mp4
• Lecture 3: State sum models. Slides and screencast of part 1 mp4

Previously given September 2009, Corfu, except lecture 1b is new. The lecture series is supported by FQXi.

State sum models, induced gravity and the spectral action.

December 2009, IHES slides of the first, brief, talk

May 2010, Bayrischzell slides of a longer talk with more detail of the proposals

May 2010, Oxford: video of the latest version of the talk, with some detail of the 2-category diagrams explaining the geometry-matter interaction in 3d (currently under development with Catherine Meusburger).

State sum models of quantum gravity.

June 2009, Wroclaw video and slides of the talk about the 4d state sum models of quantum gravity (for video, scroll down to #6). The talk starts with a general introduction to the ideas of spin foam models.

March 2011, Queen Mary, updated version of the slides of this talk, with pictures.

Knots and links in braided quantum field theory.

August 2008, Oxford, video of blackboard talk. I explain some aspects of braided quantum field theory: how it is a generating function of knots and links, and also a little about the relation to 3d quantum gravity.  The physics is first. If you want the mathematical part, fast-forward to where I clear the board.