This course will be aimed at the least experienced portion of the audience so will depend somewhat on the audience. I will hope to cover:

- the three Baez-Dolan Hypotheses, explaining their motivation and the evidence suggesting them
- the periodic table, different ways of moving round it in all sorts of directions
- cobordisms and cobordisms with corners as a motivating and guiding example, the work done in this direction
- the issues involved with defining n-categories with duals, together with what is known and not known in low dimensions

Ideologically, I will emphasise the following viewpoints:
- looking at higher-dimensional structures we know are there, and characterising what those are, rather than just coming up with definitions abstractly

- the importance of working things out very precisely in low dimensions, and indeed at all (rather than just making broad sweeping theories, though these are important too)

- the importance of a theory that is actually useable somehow, rather than something so abstract that we have no idea what it looks like

Reading list

• J. Baez and J. Dolan, Higher-dimensional algebra and topological quantum
  field theory, Jour. Math. Phys., 1995, 36:6073--6105
• J. Baez and J. Dolan, Categorification, in Higher Category Theory, eds.
  Ezra Getzler and Mikhail Kapranov, Contemp. Math. 230, American
  Mathematical Society, Providence, Rhode Island, 1998, pp. 1-36.
• J. Baez and L. Langford, Higher-dimensional algebra IV: 2-tangles, Adv.
  Math., 2003, 180:705--764P.
• Freyd and D. Yetter, Braided compact closed categories with
  applications to low dimensional topology, Adv. Math., 1989, 77:156--182
• M. C. Shum, Tortile Tensor Categories, Ph.D. Thesis, Macquarie University 1989