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)
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.
TQFT from Induced Representations: From the workshop
on Higher Gauge Theory, TQFT, and Categorification, Cardiff University, May 2011. This emphasizes the representation theoretic aspects
TQFT from (Higher) Gauge Theories: From the workshop
on Higher Gauge Theory,
TQFT, and Quantum Gravity that I helped organize at IST in Feb
- 2-Linearization in Physics and Topology: A talk given at the XIX Oporto Meeting in Faro, Portugal.
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
Relating to 2-groupoids and higher gauge theory
From the Seminar on Groupoids/Stacks/Algebras
Relating to the Quantum Harmonic Oscillator