Jeffrey Morton

Current

I am a postdoctoral fellow in the Department of Mathematics at the University of Western Ontario, working with Dan Christensen. My main research interests are mathematical physics and category theory. In particular, I have been interested in how "higher-algebraic" ideas from category theory can illuminate questions in quantum gravity and the foundations of quantum mechanics.

I also now have a blog

Seminar

I am currently organizing a Seminar on Stacks, Groupoids and Algebras.

Teaching

I am currently teaching Math 3132B/9021B - General Topology.

• (Fall 2007) General Topology (404a) (course webpage).
• (Winter 2008) Complex Variables (227b) (course webpage).
• (Fall 2008, 2009) Methods of Matrix Algebra (1229A) (2008 and 2009)
• (Winter 2009) Complex Variables (2212b) (course webpage)

Curriculum Vitae

• My CV proper (postscript and PDF)
• My research statement (postscript and PDF)
• My teaching statement (postscript and PDF)
• A list of my publications (postscript and PDF)

Research

Papers

• 2-Vector Spaces and Groupoids 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. (There's a more recent revision, also)
• Double Bicategories and Double Cospans (Recently accepted by the Journal of Homotopy and Related Structures) 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 (Hosted at Theory and Applications of Categories - also available on the archive 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:
  • Topological and Lie Groupoids, C*-Algebras and Stacks: A talk given at the seminar on this topic I am running at UWO.
  • 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.
  • A talk about the categorified harmonic oscillator which I gave at the International Category Theory Conference at White Point, Nova Scotia in June 2006.
  • Slides for a talk I gave for for my oral qualifying exam in May 2005
• Relating to my Ph.D. thesis:
  • 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.

Theses

• My Ph.D. thesis: Extended TQFT's and Quantum Gravity. The idea here is to categorify Topological Quantum Field Theories in a particular setting, and show that the result gives, in one special case, the Ponzano-Regge model of Euclidean quantum gravity.
• My Masters thesis: Existence and Nonexistence Theorems for Solutions of the Einstein-Dirac-Maxwell Equations.

Education

Ph.D - University of California, Riverside

I received my Ph.D. in June 2007 from the Mathematics Department of the University of California, Riverside, where my advisor was Dr. John Baez. My dissertation was entitled "Extended TQFT's And Quantum Gravity".

M.Sc - McGill University

I received an M.Sc. in February 2001 from McGill University, in the Department of Mathematics and Statistics. My Masters Thesis was entitled "Existence and Nonexistence Theorems for Solutions of the Einstein-Dirac-Maxwell Equations", and was written under the supervision of Dr. Niky Kamran.

B.Math - University of Waterloo

In May 1998, I acquired a B.Math. (Bachelor of Mathematics) from the Math Faculty at the University of Waterloo, with a double major in Pure Mathematics and Combinatorics and Optimization.