Matt Daws, University of Leeds: Algebraic quantum groups to compact quantum groups
I will discuss the notion of an "algebraic quantum group", in the sense of van Daele- an axiomatic approach to quantum groups with invariant measures(so not, perhaps, what algebraists might say a "quantum group" is). These hide the analytic complications of the operator algebra approach, but can only capture certain examples. I will then concentrate on the compact case, discuss relations with purely C*-algebraic approaches, and talk about morphisms.
Biswarup Das, University of Leeds: Quantum automorphisms of finite spaces
It is a well-known fact that alll automorphisms of the matrix algebra M_n(C) are inner and are given by the adjoint action of unitary matrices. To put it in another way, the automorphism group of M_n(C) is PU(n), the projective version of the unitary group. This can be framed in the language of automorphic coactions of the (abelian) quantum group C(PU(n)) on the C* algebra C(M_n(C)), where C(X) is the algebra of continuous functions on a topological space X. We will address the question "Can there exists genuine (non-abelian) quantum groups which has automorphic coactions on M_n(C)?" This will lead to the notion of Quantum automorphism group, initiated by S. Wang in 1988.
Stefan Kolb, University of Newcastle: Quantum symmetric Kac-Moody pairs
Quantum symmetric pairs for semisimple Lie algebras were invented in the 90s by M. Noumi, G. Letzter, and others to translate harmonic analysis on symmetric spaces to the quantum group setting. Examples of infinite dimensional (Kac-Moody) versions of this theory appeared in the study of quantum integrable systems with boundary. In this talk I will try to sketch these origins and give an overview over a general theory of quantum group analogs of symmetric pairs for involutions of the second kind of symmetrisable Kac-Moody algebras.