We will start with the basic definitions of Formal Group Laws (FGL), and homomorphisms between them. Later we will move to the question of classification and results of Lazard on the topic. After that we will discuss FLGs over the p-local integers and the theory of p-typical FGLs. This will lead to the definition of the height of a FGL, which we will use to classify FGLs over finite fields. The question of universal deformations and Lubin-Tate theory will be discussed here. All this should take about 6 weeks. The rest of the quarter will be devoted to the relationship of this theory to topology: We will discuss exotic cohomology theories like MU, BP and Morava K-theories K(n). Work of Quillen and Landweber will be discussed. If we still have time, we will go into the spectra E_n defined by Hopkins and Miller.

References:

Strickland - Formal Groups
Kochman - Bordism, Stable Homotopy, and Adams Spectral Sequences
Fröhlich - Formal Groups
Hazewinkel - Formal Groups and Applications
Ravenel - Complex Cobordism and Stable Homotopy Groups of Spheres
Serre - Lie Algebras and Lie Groups
Quillen - An elementary proof of some results of cobordism theory using Steenrod operations
Iwasawa - Local class field theory
Greenberg - Thesis

Schedule:

01/09 - Nitu Kitchloo - Introduction and orginazation of talks
01/16 - Joey Reed - FGL's over Q, examples, exp/log, Lazard's theorem
01/23 - Ben Cooper - p-typical FGLs, classification using p-series
01/30 - Dan Budreau - FGLs over \bar{F}_p, height, classification, examples, Honda FGLs
02/06 - Nitu Kitchloo - End_{\bar{F}_p}}(H(n)), universal deformations of H(n), Lubin-Tate Theory
02/13 - Nitu Kitchloo - cont'd
02/20 - Maia Averett - MU, BP, Milnor's computation of MU_*, Quillen's Theorem
02/27 - Maia Averett - Landweber exactness, examples, Morava k-theories
03/06 - Henning Hohnhold - Hopkins-Miller theories E_n, action of End{\bar{F}_p}}(H(n))