Abstract:
In my talk I will explain how to study the long-term behaviour of finitely generated
random walks on Fuchsian groups. This is a very rich topic which highliights a deep connections between probability and
geometric group theory. In particular, we will discuss the singularity of the harmonic measure
for nearest-neighbour random walks on cocompact Fuchsian groups with "nice" fundamental domains. If time permits,
we will discuss the latest developments related to the classification of hitting measures with respect to actions of Fuchsian groups on $S^1$.
