**Thomas Koberda**

University of Virginia, USA

August 10, 2017

**The free product structure of diffeomorphism groups**:
I will discuss some aspects of the algebraic structure of finitely
generated groups of diffeomorphisms of compact one-manifolds. In
articular, we show that if $G$ is not virtually metabelian then (G imes Z)*Z cannot act faithfully by C^2 diffeomorphisms on a compact
one-manifold. Among the consequences of this result is a completion of the classification of right-angled Artin groups which admit faithful
C^{infty} actions on the circle, a program initiated together with H.
Baik and S. Kim. This represents joint work with S. Kim.