|Date||Apr 04, 2023|
Beginning from 2-dimensional hyperbolic geometry, we present various constructions of the Teichmuller space, in perspective of hyperbolic geometry and as a space of representations. Regarding the Teichmuller space as a space of representations brings us to higher Teichmuller spaces. As direct descendants of the classical Teichmuller space, Hitchin components are the most well-known examples of higher Teichmuller spaces. At the end of the talk, we discuss some properties of Hitchin components inherited from the Teichmuller space.