Character varieties of surface groups

Short introductory talks.

The space of homomorphism of a surface group into SL(n,R) up to conjugation is called the character variety. It has a distinguished connected component, the Hitchin component, which is an instance of a "higher Teichmüller space". I am interested in the arithmetic properties of the Hitchin component. In this talk, I will discuss its Q-points and the Z-points and present some open questions that I am thinking about.