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 Bordn 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