Michael Pandazis presented Fenchel-Nielsen parametrization of the Teichmuller space of a compact surface.
Jessica Liu presented the proof that the set of hyperbolic geodesics which self-intersect in at most k points has Hausdorff dimension 1 on a compact hyperbolic surface.
I gave a talk on shear coordinates for the Farey tesselation. Casey Whitney talked about flip graphs for infinite surfaces. Ajith Nair talked about Minkowski ?-function.
We discussed shear coordinates for punctured surfaces.
Michael gave a presentation of Wolpert’s result on the length of closed geodesics under quasiconformal maps.
We discussed types of isometries of the hyperbolic plane.
We finished the proof of the Collar Theorem.
Xinlong successfully defended his PhD thesis titled “Differentiability of the Liouville Map via Geodesic Currents”. Congratulations Xinlong!!
Today we discussed the statement and corollaries of the Collar Lemma. Then we started to build the necessary tools for the proof. Next time we will finish the proof.
We held the first Graduate Workshop meeting today. We had an overview of Teichmuller spaces and discussed the direction of of the workshop.