Title: Locally compact quantum groups: introduction, examples, and some recent results
Abstract: The theory of locally compact quantum groups grew out of the need to extend Pontryagin's duality for locally compact abelian groups to a wider class of objects, as well as from a modern "quantum" point of view suggesting the replacement of some algebras of functions on a group by non-commutative objects, namely operator algebras. In this talk we will give an introduction to locally compact quantum groups: present the rationale and the definitions, give examples, discuss constructions, and explain how the theory is related to other branches of mathematics. Then we will describe a few recent results on lattices in locally compact quantum groups, emphasizing the case of the Drinfeld double (joint work with Michael Brannan and Alexandru Chirvasitu). No background in operator algebras will be assumed.