Alternatively have a look at the program.

## (joint IMPRS-Minicourse and Cobordism Hypothesis Seminar) Overview of the cobordism hypothesis

The cobordism hypothesis, conjectured by Baez-Dolan and proven by Lurie, provides a classification

of fully local topological field theories. In this talk we will describe an approach to proving the

cobordism hypothesis which closely follows Lurie's original sketch, but which also incorporates

some more recent simplifications.

This first overview talk is being jointly held with IMPRS, and will be more accessible. I will

assume that the audience is familiar with basic category theory, some parts of abstract homotopy

theory, and with smooth manifolds.

## A categorical approach to the h-principle

We will describe an approach to the h-principle tailored to categorically minded topologists. This will

form the basis for proving that Igusa's space of framed generalized Morse functions is contractible,

the key geometric step in the proof of the cobordism hypothesis.

Note that this will be an extended talk starting at the earlier time of 14:00.

## The $(\infty,n)$-category of cobordisms

I will explain how to construct the symmetric monoidal $(\infty,n)$-category of

cobordisms using (complete) $n$-fold Segal spaces as a model, following work by

Galatius-Madsen-Tillmann-Weiss and Lurie. Its homotopy category and bicategory

recover the usual cobordism category and the cobordism bicategory defined by

Schommer-Pries. Finally, this allows to give a precise definition and explicitly

construct examples of fully extended topological field theories in the sense of

Lurie's formulation of the Cobordism Hypothesis.

## Lurie's induction step

In this talk I will explain the elaborate induction step in Lurie's approach to the cobordism hypothesis.

## Generalized Morse functions satisfy the h-principle

## Contractibility of the space of framed Igusa functions

## Leftovers

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