Selected Talks

My main research interests are mathematical physics, topology, and category theory, and in particular, how "higher-algebraic" ideas from category theory can illuminate questions in quantum gravity and the foundations of quantum mechanics. This has connections to Witten-type path-integral invariants for manifolds, combinatorics, representation theory, and more.

Relating to ETQFT's and Gravity

• Extended TQFT in a Bimodule Category, given at Workshop on Representation Theoretical and Categorical Structures in Quantum Geometry and Conformal Field Theory in Erlangen, Germany - October 2011. This one contains discussion of the cohomological twisting of the span category which is used to reproduce the twisted Dijkgraaf-Witten model.
• Extended Field Theories and Higher Gauge Theory, from Quantum Theory and Gravitation, Zurich, 2011. This one is brief, aimed at a physics audience (more or less)
• Extended TQFT from Gauge Theories: From the workshop Higher Structures in Geometry and Topology V, Hamburg, May 2011 - this one explains the infinite-dimensional case in the most detail.
• Extended TQFT from Induced Representations: From the workshop on Higher Gauge Theory, TQFT, and Categorification, Cardiff University, May 2011. This emphasizes the representation theoretic aspects
• Extended TQFT from (Higher) Gauge Theories: From the workshop on Higher Gauge Theory, TQFT, and Quantum Gravity that I helped organize at IST in Feb 2011.
• 2-Linearization in Physics and Topology: A talk given at the XIX Oporto Meeting in Faro, Portugal.
• Slides for a talk given at the conference "Connections in Geometry and Physics" organized by the Perimeter Institute for Theoretical Physics, the Fields Institute, and the University of Waterloo, held at the Perimeter Institute in Waterloo, Canada, May 8-10, 2009

Relating to spans, groupoids, and 2-vector spaces

• Groupoidification in Physics: Notes (and slides) for a talk at IST Nov 2010
• Groupoidification and 2-Linearization, Discrete and Smooth: A talk given at CAMGSD in July 2010.
• Groupoidification and 2-Linearization: A talk given at the mathematics colloquium while I was visiting at Dalhousie in September of 2009.
• Groupoids, Spans and Physics: a talk given at U of Ottawa, January 2009. Presents 1-vector space and 2-vector space views of groupoidified physics.
• 2-Vector Spaces and Groupoids: a talk given for GroupoidFest '08 at UCR, November 2008.

Relating to 2-groupoids and higher gauge theory

• 2-Group Symmetries on Moduli Spaces in Higher Gauge Theory
: slides for a talk given at the Workshop on Higher Gauge Theory and Higher Quantization, in Edinburgh, Scotland, June 2014.
• Higher Gauge Theory and 2-Group Actions (Joint with Roger Picken): Slides for a talk given at Masaryk University, in Brno, Czech Republic, December 2012.

From the Seminar on Groupoids/Stacks/Algebras

• Topological and Lie Groupoids, C*-Algebras and Stacks: An intorductory talk introducing groupoids as the link between two ways of generalizing "space": stacks, and noncommutative geometry.
• Groupoid Representation Theory: The basics of groupoid representations, and leading up to a main theorem about Morita equivalence in different categories.

Relating to the Quantum Harmonic Oscillator

• "Categorification and Groupoidification of the Heisenberg Algebra", a talk given at Higher Structures in China III, in Changchun, China in Aug 2012. This relates the groupoidifications of the quantum harmonic oscillator to Khovanov's categorification of the Heisenberg algebra.
• "Two Categorifications of the Heisenberg Algebra", a talk given at Higher Structures 2011 in Goettingen, November 2011.
• A talk about the categorified harmonic oscillator which I gave at the International Category Theory Conference at White Point, Nova Scotia in June 2006.