Andrey Lazarev (University of Bristol)
A.Lazarev@bristol.ac.uk
The category of spectra is the main object of study for stable homotopy theorists. One can consider this category as the nicest, most algebraicizable part of the category of topological spaces.
Recently there has been a major development in the subject. It was proved that the stable category admits a strictly associative and commutative product (previously it was known to exist only up to homotopy). This allowed a wholesale importation of the commutative algebra methods into homotopy theory. In particular one can consider the (usual) derived categories of modules and algebras as (very) special cases of the topological construction.
My talk will be concerned with homotopy theory of A-infinity ring spectra. An A-infinity ring spectrum is a natural generalization of a differential graded algebra. I will discuss moduli spaces of multiplicative maps, their relation to topological Hochschild homology and show how this leads to interesting new infinite loop spaces.