My Background
Education
Previous Employment
Previously, I have been
at CAMGSD, a research
centre in the Mathematics department of
the Instituto Superior Tecnico in
Lisbon, Portugal, and before that in
the Department of Mathematics at
the University of Western Ontario,
working with Dan Christensen.
I have also taught at the college and university level as T.A. and primary
instructor for over ten years. I have taught at:
- McGill University (Montreal); T.A. 1998-2000; Lecturer, 2001
- Dawson College (Montreal); Lecturer, 2001-2002
- The University of California (Riverside); T.A. 2002-2007
- The University of Western Ontario (London, Canada); Postdoc and Assistant Professor, 2007-2010
Curriculum Vitae
Some materials related to my CV:
Research
Research Papers
The Categorified Heisenberg Algebra I: A Combinatorial Representation
(with Jamie Vicary, arXiv:1207.2054)
Demonstrates that groupoidification of the Heisenberg algebra
gives a concrete model of Khovanov's diagrammatic calculus, and suggests
how this might work for other cases. First part of two - second
forthcoming. Extended TQFT, Gauge Theory, and 2-Linearization
(arXiv:1003.5603)
Uses 2-linearization (see "2-Vector Spaces and Groupoids")
to build an Extended TQFT associated to a discrete gauge group. A
special case, for closed manifolds, yields the untwisted
Dijkgraaf-Witten model. 2-Vector Spaces and Groupoids
(arXiv:0810.2361; Applied
Categorical Structures; DOI: 10.1007/s10485-010-9225-0)
Constructs a 2-functor from the bicategory of spans of
groupoids into the bicategory of 2-Vector spaces. I
interpret this as a kind of categorified version of quantization of a
physical system. Double Bicategories and Double Cospans
(arXiv:math.CT/0611930;
Journal of Homotopy and Related Structures, Vol. 4(2009), No. 1,
pp. 389-428)
Describes a kind of weak cubical 2-category, how a
construction using cospans (or spans) gives examples, and how they
relate to more familiar 2-categories. Categorified Algebra and Quantum Mechanics Theory and
Applications of Categories
(arXiv:math.QA/0601458,
Theory and Applications of Categories, Vol. 16, 2006, No. 29, pp
785-854.)
Describes the quantum harmonic oscillator in terms of "stuff
types", related to combinatorial species, and gives a combinatorial
interpretation of Feynman diagrams.
Expository Papers
These are some shorter papers explaining some of the same material as
in the above, but for different audiences.
Cubical n-Categories and Finite Limits Theories (arXiv:1001.2628; unpublished)
An expository piece explaining how the double cospan
construction in math.CT/0611930 may be seen in terms of taking models
of finite limits theories. Higher cubical n-categories can be
constructed by iteratively taking models of a theory of
categories/bicategories etc.)
Groupoidification and Categorification in Physics (hosted here)
Originally written for a philosophy of science proceedings,
but not used. Talks about the significance of various forms of
categorification as explanations (i.e. descriptive accounts) of
mathematical structures in physics. Makes (possibly naive)
philosophical remarks about how this relates to structural
realism.
Selected Talks
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
Relating to 2-groupoids and higher gauge theory
From the Seminar on Groupoids/Stacks/Algebras
Relating to the Quantum Harmonic Oscillator
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