Abstract: In this series of lectures, we will discuss basic examples of compact quantum groups and their (finite dimensional) representations. We will start with reviewing the classical theory. We shall classify all finite dimensional irreducible representations of compact Lie groups SU(2) and SU(3). Then we will proceed to the general theory of representation of compact Lie groups and will discuss several important results including the highest weight theory, the Peter-Weyl decomposition theorem, and also the Borel-Weil-Bott construction of representations. Finally, we will see how much of the theory holds in the quantum case.

Abstract: Equivariant spectra have received a good deal of attention lately due to their central role in the Hill-Hopklins-Ravenel proof of the Kervaire invariant one problem. I will describe joint work with Peter May that provides an alternative model for equivariant spectra (indexed on a complete G-universe).