Graduate Student Seminar- Critical points for the Hausdorff dimension of pair of pants
Friday, April 3, 2026
2:00 pm - 3:00 pm
Date: April 3, (Friday) 2-3 pm
Location: Rome 771
Speaker: Chengti Yang , GWU
Title: Graduate Student Seminar- Critical points for the Hausdorff dimension of pair of pants
Abstract: This presentation is based on the paper Critical points for the Hausdorff dimension of pairs of pants by Mark Pollicott and Polina Vytnova. We study the dependence of the Hausdorff dimension of the limit set of a hyperbolic Fuchsian group on the geometry of the associated Riemann surface.
Specifically, we focus on the “pair of pants” surface, parameterized by the lengths of its three boundary geodesics, b = (b1, b2, b3).
We will discuss the behavior of the dimension function dim(b) subject to restrictions on the total boundary length. A key analytical result to be presented is the identification of seven specific points, including the center of the moduli space, as critical points of the dimension function dim(b). Furthermore, we will demonstrate that under certain conditions, this central configuration serves as a local minimum.
Finally, we will compare two numerical methods for computing the Hausdorff dimension: the classical algorithm by McMullen and a method based on the zeros of the Selberg Zeta Function. We will demonstrate that the Selberg Zeta approach offers superior efficiency near the center of the moduli space.
Graduate Student Seminar is mandatory for all math graduate students.