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.
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.
Everyone who wishes to participate is welcome, particularly postgraduate students. We shall operate the usual criterea for assistance with travel expenses, but beneficiaries will need to complete the standard UM green form. Those who qualify should therefore come armed with their NI numbers, and details of their UK bank accounts. Please email MIMS secretary Louise Stait if you are interested in attending, so that we can cater for appropriate numbers.
The meeting is jointly supported by the London Mathematical Society and MIMS.