# TTT52: Manchester

School of Mathematics, University of Manchester.

Everyone who wished to participate was welcome, particularly postgraduate students.

## Date

6 December 2005

## Speakers

Andrew Baker (Glasgow)

Gamma-cohomology of rings of numerical polynomials, and E-infinity structures on K-theory

There is an obstruction theory for E-infinity structures on commutative ring spectra which makes use of Gamma-cohomology, defined by Robinson and Whitehouse. This is a cohomology theory for commutative rings that is closely related to Andre-Quillen cohomology as well as to the obstruction theory of Goerss and Hopkins.

Francis Clarke (Swansea)

Enumerating abelian groups

How many finite abelian groups are there? More precisely, given a finite set, how many of the binary operations on it make it into an abelian group? A recursion for this function is a key component in Cohen-Lenstra heuristics on the distribution of class groups. I shall give a bijective proof of the recursion in which the essential ingredient is a piece of labelled homological algebra.

Andrey Lazarev (Bristol)

## Further information

The meeting was jointly supported by the London Mathematical Society and MIMS.