Chris Heath: Mathematics stuff

Degrees and Universities

My last completed degree is a masters degree with a major in mathematics (November 1995). That was in the Department of Mathematics at the University of Auckland.

In the first half of 1996 I temporarily started a PhD in mathematics at Auckland, and during that time I taught a first-year calculus and algebra class for economics students.

In August 1996, I moved to the University of Michigan, Ann Arbor. I spent 4 years in the PhD program in the Department of Mathematics, but I decided not to finish it.

Research interests

In Auckland, my PhD supervisor was Dr. Jianbei An, and I was working on Dade's conjecture for some particular finite simple groups. Admittedly, I didn't get very far with it, because I needed to learn a lot of basics first. (In fact I didn't ever get past the basics!)

My master's project was on Topological Quantum Field Theories (TQFT's) where I was working under the supervision of Professor David Gauld. I grew interested in the TQFT topic while attending the knots@huia workshop in 1994 (see the diary below). The main papers I was working from are

  1. C. Blanchet, N. Habegger, G. Masbaum, P. Vogel, Three-manifold invariants derived from the Kauffman bracket, Topology 31 (1992) 685–699.
  2. C. Blanchet, N. Habegger, G. Masbaum, P. Vogel, Topological Quantum Field Theories derived from the Kauffman bracket, preprint May 12, 1994.
Somehow or other these theories are related to Quantum Field Theories in physics, but I never managed to find out how (even to a slight degree). My research topic at the University of Michigan led me to some insights in this, but not much.

Diary — events past and future

  1. In December 1994, I attended a workshop known locally as "knots@huia". As the name suggests, the theme was knots, and the place was at Huia, a little bit west of Auckland. The idea of this workshop was spawned by Professor Vaughan Jones and was brought into being by him and David Gauld among others. It was at this workshop that Nathan Habegger gave a series of four lectures giving a summary of his papers (above) which describe some explicit examples of TQFT's.
  2. In January 5–13 1996 there was another of Jones' workshop/conferences, this time held in Tolaga Bay, north of Gisborne. The theme this time was solvable models of various kinds. (Here the term "models" refers to models of statistical mechanical problems such as magnetisation on a crystal lattice.)
  3. In Jan 22 – Feb 9 1996, I attended a workshop at ANU, Canberra, Australia. It is called a "workshop on algebra, geometry and topology", especially for masters and doctoral students. Lots of it was really good, especially the quantum groups series presented by Arun Ram. He was entertaining, and the math interests me.

My work-load

This winter term, I am teaching an introductory calculus course Math 116. Lots of work for me, but I always enjoy teaching. I am also taking a course in Characteristic Classes (696), another in Algebraic Geometry (632), and a reading course in K-theory.

Some math-oriented links

Random tidbit

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Last changed 1 Oct 2000