Bert Guillou

I am currently a sixth-year graduate student interested in algebraic topology. My advisor is Peter May. I received undergraduate degrees in math and philosophy from the University of Michigan.

My topic exam was in A^1-homotopy theory. Now usually referred to as motivic homotopy theory, this is a program begun by Fabien Morel and Vladimir Voevodsky (see the webpage for the motivic homotopy theory seminar held at the Institute for Advanced Study). The idea is to develop a "homotopy theory" for smooth schemes over a nice (Noetherian) base S, in which the affine line A^1 would play the role of the unit interval. Once the theory has been set up, one can then use the heavy machinery from homotopy theory to answer questions in algebra and algebraic geometry. In particular, Voevodsky constructed Steenrod operations for motivic cohomology and used this to prove the Milnor conjecture.

Proseminar talk notes:

Algebraic K-theory: Intro (11/11/04).
Unstable A^1-homotopy theory (3/2/05).
Stable A^1-homotopy theory (3/4/05).
Algebraic K-theory: +=Q (11/15/05-11/22/05).
Kan's Ex^\infty Functor (10/11/06).
Models for Equivariant Homotopy Theory (11/16/06).
The Bousfield-Kan Spectral Sequence (1/25/07-1/30/07).

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