Title: Introduction to motivic homotopy theory
Speaker: Marc Hoyois
Speaker Info: Northwestern University
One can do homotopy theory with algebraic varieties by casting the affine line A1 in the role of the interval [0,1]. However, this is like attempting to do homotopy theory using only manifolds, without having more general topological spaces at hand. In the 90s Voevodsky came up with a suitable notion of space in algebraic geometry. Since then, motivic homotopy theory has been used to prove several long-standing conjectures in number theory and representation theory, and has become a field of study in its own right. I will explain Voevodsky's definition of motivic space, and illustrate the concept by means of examples and computations.Date: Thursday, May 12, 2011
Time permitting, I will talk about the stable theory and show how it leads to an easy proof of the Riemann hypothesis.