Spectra, Complex Oriented Cohomology Theories, and Formal Group Laws

This talk is a first introduction to complex oriented cohomology theories. We begin by introducing the 1-category of (symmetric) spectra, giving some basic definitions and properties, and their relationship with generalized cohomology theories, i.e. Brown's representation theorem. Of generalized cohomology theories, we focus then on the class of complex oriented ones. Finally, we introduce the notion of formal group law and sketch its connection to complex oriented cohomology theories.