Seminars & Colloquia Calendar
Solving' the simplest nontrivial dynamical systems: Straight lines on compact flat surfaces
Jozsef Beck - Rutgers University
Location: Hill 705
Date & time: Thursday, 01 February 2018 at 12:00PM - 1:00PM
Abstract: Consider a square-tiled plane region (=connected subset of the square lattice), and glue together the pairs of ``opposite" edges: this gives a very rich infinite family of flat surfaces (with conic singular points). For every member of this family of surfaces we can describe the equidistribution of the geodesics (=basically straight lines, since the surface is flat) in terms of the continued fraction digits of the initial slope, and in terms of the shape of the region. More precisely, we describe the mostly polynomial ``fluctuations of the irregularities" with an explicit formula which heavily depends on these numerical parameters.