Mona Merling
SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Mona Merling Abstract. Quillen's algebraic Ktheory of rings and schemes has deep connections to problems in number theory, and Waldhausen's Atheory, an extension of algebraic Ktheory to spaces, is central to the classification of diffeomorphisms of manifolds. I will discuss how to encode the extra information given by a group action on the input of algebraic Ktheory. I will focus on a joint project with C. Malkiewich aimed at constructing an equivariant generalization of Atheory in the case when the input is a space with group action, which should have rich geometric applications by analogy with the nonequivariant case. This project fits into a longterm research program aimed at establishing a chain of homotopytheoretic constructions that relate the behavior of compact Gmanifolds to that of their underlying equivariant homotopy types.
