Quantum groups versus combinatorics in free probability

I will give a general introduction to compact matrix quantum groups and then focus in a survey talk on those of combinatorial type. These include Banica-Speicher's orthogonal easy quantum groups using partitions; the unitary easy quantum groups introduced by Pierre Tarrago and myself using partitions with monochromatic colored points; the spatial partition quantum groups introduced by Guillaume Cébron and myself using three-dimensional partitions; and finally the partial commutative quantum groups introduced by Roland Speicher and myself fitting to the mixtures of classical and free independence by Mlotkowski and Speicher-Wysoczanski.Non UBCUnreviewedAuthor affiliation: Saarland UniversityFacult