Beyond motivic homotopy theory
Beyond motivic homotopy theory

Dan Isaksen, Wayne State University
Fine Hall 110
I will describes Hopf's classical construction of some essential maps between spheres. These maps possess some curious equivariant properties. I will use these examples to motivate the study of motivic homotopy theory, and to propose new homotopy theories that ought to be even more interesting than motivic homotopy theory.
I will also describe some recent stunning applications of motivic homotopy theory to classical homotopy theory. Why should a homotopy theory of algebraic varieties be so useful for studying ordinary topological spaces? I will make a first attempt at answering this philosophical question by giving a topological model for cellular 2complete stable Cmotivic homotopy theory.