University of Sheffield

Thursday

October 21, 2010

This will be a special meeting aimed at new postgraduates and post docs, who are particularly encouraged to attend.

Speakers: David Barnes (Sheffield), Alastair Darby (Manchester), Harry Ullman (Sheffield), Nick Gurski (Sheffield).

- 10:45 Tea and Coffee
- 11:15
**David Barnes**: Spectra and Stable Homotopy Theory - 12:00 Lunch
- 13:30
**Alastair Darby**: TBA - 14:15 Tea, Coffee and discussion
- 14:45
**Harry Ullman**: Equivariant Homotopy Theory - 15:30 Tea, Coffee and discussion
- 16:00
**Nick Gurski**: Enriched Categories as Models for Spaces

After the last talk we expect to go for dinner and drinks at some place nearby.

David Barnes: **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 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**

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.

Anyone who wishes to participate is welcome: we shall operate the usual criteria for assistance with travel expenses, but beneficiaries will need to complete the standard forms, and should come armed with NI numbers and details of UK bank accounts. This usually means that travel costs for topologists from Leicester and Manchester will be covered, participants from elsewhere may receive some contribution towards their travel costs, but are encouraged to seek support from other sources.

We expect to assemble for tea and coffee in I15, Floor 5, from 10:45 am until the first talk. Each lecture will take place in Room J11 of the Hicks Building, Hounsfield Road, Sheffield. Tea and Coffee will be served in the common room I15.

If you are interested in attending, or for further information, email David Barnes d.j.barnes@sheffield.ac.uk or Harry Ullman h.ullman@sheffield.ac.uk if you are interested, so we can make approximately the right amount of tea and coffee.

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

To TTT74

To TTT76