Thomas Budzinski

What is the minimal possible diameter of a hyperbolic surface (i.e. with constant curvature equal to -1) of genus g? We will prove that it is asymptotic to log(g). While the lower bound follows from a simple volume growth argument, the upper bound is...

Abstract: A triangulation of a surface is a way to divide it into a finite number of triangles. Let us pick a random triangulation uniformly among all those with a fixed size and genus. What can be said about the behaviour of these random geometric...