# Seminars & Colloquia Calendar

Mathematical Physics Seminar

## 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.

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