Distribution of simple closed geodesics on a closed hyperbolic surface.

Speaker : Bidyut Sanki

Date : 10th June, 2014 (Tuesday)

Time : 09:15 pm – 10:15 pm

Venue : Lecture Hall I, Department of Mathematics

Abstract : It is a fact in hyperbolic geometry that, the union of closed geodesics on a closed hyperbolic surface is dense. The situation is quite different if one restrict one’s consideration to the simple closed geodesics: Birman and Series proved that the union of all simple (without self intersection) closed geodesics is a nowhere dense set. In this talk, we will prove that, there exists a positive real number $r_g$ depending only on the genus g, such that, any closed hyperbolic surface of genus g contains a disc of radius $r_g$ into which simple closed geodesics do not enter.

Area: Geometry