Instructor: Peter Teichner

Lectures: Tu 11:00-12:30, 740 Evans

Recommended Reading: Expository article on topological field theories, by Jacob Lurie [JL].

Office Hours: Tu 2:00-3:30, 703 Evans

Syllabus: We’ll study the space of topological field theories as defined by Mike Hopkins and Jacob Lurie. These are symmetric monoidal d-functors from the d-category of manifolds (of dimensions 0 through d) into another target d-category. In fact, it is better to work with infinity d-categories in the sense that the spaces of diffeomorphisms of d-manifolds are taken into account.

The main result is a generalized version of the Baez-Dolan cobordism hypothesis, computing this space of topological field theories for framed manifolds in terms of the fully dualizable objects in the target infinity d-category.

Schedule of talks: (section numbers refer to [JL] above)

Jan. 20 Peter Teichner, Overview of Results and Definitions

Jan. 27 Martin Olbermann, Introduction, Section 1

Feb. 3 Chris Schommer-Pries, Complete Segal Spaces, 2.1

Feb. 10 Chris Schommer-Pries, Iterated Segal Spaces, 2.1

Feb. 17 Peter Teichner, Bordism categories as Segal Spaces, 2.2

Feb. 24 Konrad Waldorf, Fully dualizable objects, 2.3

March 3 Konrad Waldorf, Fully dualizable objects, 2.3

March 10 Alan Tarr, The Cobordism Hypothesis, 2.4

March 17 Kevin Lin, The Mumford Conjecture, 2.5

spring break

March 31 Dmitri Pavlov, 3.1

April 7 Constantin Teleman, 3.2

April 14 Kevin Walker, 3.3

April 21 Chris Douglas, 3.4

April 28, Nate Watson, 3.5

May 5, Martin Olbermann, Section 3.5