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Abstracts for Cobordism hypothesis seminar

Alternatively have a look at the program.

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

Posted in
Speaker: 
Chris Schommer-Pries
Affiliation: 
MPIM
Date: 
Wed, 2016-05-04 14:30 - 16:00
Location: 
MPIM Seminar Room

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

Posted in
Speaker: 
Chris Schommer-Pries
Affiliation: 
MPIM
Date: 
Wed, 2016-05-18 14:00 - 16:00
Location: 
MPIM Seminar Room

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

Posted in
Speaker: 
Claudia Scheimbauer
Affiliation: 
MPIM
Date: 
Wed, 2016-05-25 14:30 - 16:00
Location: 
MPIM Seminar Room

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

Posted in
Speaker: 
Claudia Scheimbauer
Affiliation: 
MPIM
Date: 
Wed, 2016-06-01 14:30 - 16:00
Location: 
MPIM Seminar Room

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

Posted in
Speaker: 
Chris Schommer-Pries
Date: 
Wed, 2016-06-08 14:00 - 16:00
Location: 
MPIM Seminar Room

Contractibility of the space of framed Igusa functions

Posted in
Speaker: 
Dennis Borisov
Affiliation: 
U of Oxford/MPIM
Date: 
Wed, 2016-06-15 14:00 - 16:00
Location: 
MPIM Seminar Room

Leftovers

Posted in
Speaker: 
Chris Schommer-Pries
Affiliation: 
MPIM
Date: 
Mon, 2016-06-20 14:00 - 16:00
Location: 
MPIM Lecture Hall
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