The first talk is an introductory talk on non-crossing partitions of a circularly ordered set based on Kreweras' original paper. A non-crossing partition of n points on a circle is a partition π such that, if you draw all the chords joining points in the same block of π, there are no crossing chords. The theory is remarkably rich and has become more and more important.
The second talk on non-crossing partitions takes up questions of enumeration: how many non-crossing partitions are there, how many have a given type, et al.