Time: 09:30
Speaker: Ali Moatadelro (Western)
Title: "Representation theory of compact quantum groups with examples, lecture 6, Irreducible representations of semisimple Lie agbras."
Room: MC 107

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.

Time: 15:30
Speaker: Clark Barwick (MIT)
Title: "Algebraic K-theory of $\infty$-categories"
Room: MC 107

Abstract: In joint work with John Rognes, we show how to transfer the technologies and results of Quillen and Waldhausen in higher algebraic $K$-theory to the context of $\infty$-categories. Analogues of the $S_{\bullet}$ and $Q$-constructions — as well as versions of the additivity, localization, and d evissage theorems — are among the results we find in this new context. As a motivation for this work, we discuss a conjecture of Hopkins, Waldhausen, and Rognes on the algebraic $K$-theory of $BP\langle n\rangle$.