# TTT75: Sheffield

Department of Pure Mathematics, the University of Sheffield.

This was a special meeting aimed at new postgraduates and postdocs.

## Date

21 October 2010

## Speakers

### David Barnes

Spectra and stable homotopy theory

Spectra and stable homotopy theory

If homotopy theory is the study of spaces up to homotopy, then stable homotopy theory is the study of homotopy theory up to 'suspension'. Suspension is a method of making spaces larger, for example the suspension of the n-sphere is the n+1-sphere.

There are many fascinating patterns and structures within homotopy theory that are only revealed when looking through the lens of stable homotopy theory, such as the Freundenthal suspension theorem. In this talk we will mention some of these patterns and introduce spectra as a way of studying spaces up to suspension.

### Alastair Darby

TBA

### Harry Ullman

Equivariant homotopy theory

Equivariant homotopy theory

Equivariant topology is the study of spaces with a group action. Prevalent throughout the theory is a striking contrast with the non-equivariant theory; things that are topologically interesting in the equivariant world may not seem so interesting when the group action is ignored.

In this talk we set up the machinery needed to build equivariant homotopy theory before detailing some of the interesting constructions used in the subject. We conclude with some startling examples of how much considering group actions impacts upon homotopy theory.

### Nick Gurski

Enriched categories as models for spaces

Enriched categories as models for spaces

Most common examples of 'naturally occurring' categories – things like the category of spaces or the category of R-modules for a ring R – are in fact enriched categories. Enriched category theory is extremely well-developed, but is often viewed as an even more obscure and arcane subject than category theory itself.

In this talk, I will approach the topic of enriched categories from a different perspective, and try to convince you that enriched categories should often be viewed as more interesting versions of things you already know about. My eventual goal will be to talk about the relationship between enriched categories and spaces.

## Further information

The meeting was partially supported by a Scheme 3 grant from the London Mathematical Society.