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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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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

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