Seminar on Cobordism
and Topological Field Theories

2009-2010

Fall and Winter:
Fridays at 12:10 pm, Surge 268

Spring: Wednesdays at
1:10 pm, Surge 268

In
this seminar we'll work through recent notes of Lurie giving an outline of his
proof of the Cobordism Hypothesis, relating cobordism classes of manifolds and
topological field theories. This work
brings together several areas of recent mathematical interest: topological
field theories, cobordisms of manifolds, and homotopical approaches to higher
categories. We'll go over basic
definitions and examples of all of the above and then work towards
understanding Lurie's proof.

Main
reference: J. Lurie, On the
classification of topological field theories.

__Schedule of talks:__

Friday,
September 25: John Baez, Introduction to the cobordism hypothesis

Friday,
October 2: Julie Bergner, Manifolds and cobordism

Friday,
October 9: Julie Bergner, Topological field theories

Friday,
October 16: Chris Carlson, Topological field theories in low dimensions

Friday,
October 23: John Huerta, A short history of the interaction between quantum
field theory and topology

Friday,
October 30: Julie Bergner, 2-Extended topological field theories

Friday,
November 6: Julie Bergner, 2-Extended topological field theories and
2-categories

If you need a crash course in
bicategories, see Tom Leinster’s “Basic bicategories.”

Friday,
November 13: John Baez, Cobordism bicategories

Friday,
November 20: Julie Bergner, Framings, dualizable objects, and the statement of
the cobordism hypothesis

Friday,
December 4: Julie Bergner, (∞,n)-categories and diffeomorphisms

Friday,
January 8: Julie Bergner, Towards a precise definition of (∞,n)-categories

Friday,
January 15: No seminar

Friday,
January 22: John Huerta, A crash course in simplicial methods

Friday,
January 29: Julie Bergner, More simplicial methods and the nerve construction

Friday,
February 5: Julie Bergner, Complete Segal spaces

Friday,
February 12: Julie Bergner, n-Fold complete Segal spaces

Friday,
February 19: Julie Bergner, Complete Segal spaces of cobordisms

Friday,
February 26: Julie Bergner, n-Fold complete Segal spaces of cobordisms and
notions of duals

Friday,
March 5: Julie Bergner, Fully dualizable objects and the precise statement of
the cobordism hypothesis

Friday,
March 12: Vasiliy Dolgushev, The cobordism hypothesis for manifolds with
structure

Wednesday,
March 31: Julie Bergner, The inductive formulation of the cobordism hypothesis

Wednesday,
April 7: Julie Bergner, Proving the cobordism hypothesis from the inductive
formulation

Wednesday,
April 14: Julie Bergner, Reducing to the unoriented cobordism hypothesis

Wednesday,
April 21: Julie Bergner, Categorical chain complexes and skeletal sequences

Wednesday,
April 28: Julie Bergner, Comparison of categorical chain complexes and skeletal
sequences

Wednesday,
May 5: Julie Bergner, Morse theory and building Bord_{n} via generators
and relations

Wednesday,
May 12: Julie Bergner, The framed function version of the cobordism hypothesis

Wednesday,
May 19: Chris Rogers, Obstruction theory (∞,n)-categories

Wednesday,
May 26: No seminar

Wednesday,
June 2: The finale

http://www.math.ucr.edu/~jbergner/cobordism.pdf Last updated: 2 June 2010