Event Type:

Number Theory Seminar

Date/Time:

Tuesday, March 8, 2022 - 10:00 to 11:00

Abstract:

In 2002, Reza Chamanara constructed a family of surfaces of infinite genus called the a-Chamanara surfaces, a \in (1, \infty). In the special case where n is a natural number, the n-Chamanara surface admits a homeomorphism the “n-Baker map” which descends down to the 2-sphere under a certain involution. The dynamical system on the 2-sphere has a dense set of periodic points which allows us to mimic the construction of the Sierpinski Carpet presented in Boronski and Oprocha’ s “On dynamics of the Sierpinski Carpet (2018)”. In this talk, I will mainly focus on topological and dynamical properties of the 2-Chamanara surface. I will sketch a relation of the system on the 2-Chamanara surface with the system of the full shift on two symbols {0,1}. Then we will briefly move to the general case of the n-Chamanara surface.

Host: