### Seminar on Cobordism and Topological Field Theories at UCR

#### Posted by Alexander Hoffnung

This quarter Julie Bergner has begun a seminar at UC Riverside on cobordisms and topological field theories. The abstract on the seminar homepage states:

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.

The main reference for this seminar is Jacob Lurie’s paper on the classification of topological field theories.

You can also see the list of scheduled speakers on the homepage. I believe the plan is that Julie will give most of the talks while others fill in once in a while.

I will try to keep posting notes from this seminar here for anyone who is interested in following along. I will start by posting the introductory lecture by John Baez, which took place about two weeks ago, and I will post a lecture every few days until we are caught up to the seminar. Then I will try to post once a week after each seminar. Christopher Walker has been kind enough to draw pictures without which these notes would be terribly hard to follow.

John begins the story with the cobordism hypothesis and the birth of $n$Cob:

The Cobordism Hypothesis.$n$Cob is the free stable ($\infty, n$)-category on a fully dualizable object.

nCob began life as a category where:

- objects are framed (compact smooth) ($n-1$)-dimensional manifolds and
- morphisms are framed (compact smooth) $n$-dimensional cobordisms.

… click here for more. Enjoy!

## Re: Seminar on Cobordism and Topological Field Theories at UCR

We’re also having a seminar on the same subject here at Stony Brook.