My Background
Education
Teaching
I have 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
Papers
Extended TQFT, Gauge Theory, and 2-Linearization (arXiv:1003.5603; submitted to Journal of Knot Theory and its Ramifications)
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.
Cubical n-Categories and Finite Limits Theories (arXiv:1001.2628; unpublished)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.)
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.
Selected Talks
Relating to spans, groupoids, and 2-vector spaces
From the Seminar on Groupoids/Stacks/Algebras
Relating to ETQFT's and Gravity
- 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
- Slides for a talk given at the quantum gravity seminar at the Perimeter Institute, Feb 28, 2008.
- Slides for my dissertation defense talk at UCR in June of 2007. This is more technical, focusing on defining terms and stating my main theorem.
Relating to the Quantum Harmonic Oscillator
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