Algebra/Topology seminar

Speaker: Mike Hopkins

Title: The Wilson space hypothesis

Abstract: In his 1972 thesis, Steve Wilson showed that the even spaces in the loop spectrum for complex cobordism have homology which is torsion free and concentrated in even degrees. By Milnor's calculation the same is true of the homotopy groups. Wilson went on to completely classify spaces whose homotopy and homology groups are free abelian and concentrated in even degrees. Such spaces became know as "Wilson spaces," and have many remarkable properties. Shorty after Wilson's thesis appeared, he and Doug Ravenel introduced the notion of "Hopf rings" and significantly developed the whole theory. Around 2012,  working with Mike Hill, it became apparent that one could formulate a fairly general "Wilson space hypothesis" and we were able to prove it some cases of equivariant homotopy theory. In this talk I will describe recent joint work with Tom Bachmann and Aravind Asok, proving the Wilson space hypothesis in motivic homotopy theory. As Tom will explain in his talk, this has many applications to classification problems on affine varieties.