Geometry and Topology Seminar

Abstract: In this talk, we will explain two recent results for Hitchin
representations.  First, it follows from the work of Bonahon-Dreyer and
Fock-Goncharov that one can construct a real-analytic parameterization for
the PSL(n,R) Hitchin component that is explicitly analogous to the
Fenchel-Nielsen coordinates on Teichmuller space. Using this
parameterization, we produce a large family of sequences in the Hitchin
component along which the topological entropy converges to 0. The second
result is joint work with Gye-Seon Lee, where we found an analog of the
collar lemma for Hitchin representations. Some geometric consequences of
these two results will also be highlighted.