ICTP Mathematics Seminar - Tuesday 23 February at 15:00

[Math Section]

M A T H E M A T I C S   S E M I N A R S  2016


Tuesday, 23 February at 15:00



M. Artigiani (University of Bristol)


Title: Lagrange spectrum of Veech surfaces

Abstract: The Lagrange spectrum is a classical object in Diophantine
approximation on the real line that has been generalised to many
different settings. In particular, recently it has been generalised to a
similar object for translation surfaces, which attracted quite some
attention in the field. We study the Lagrange spectrum in the contest of
Veech translation surfaces. These are particular translation surfaces
with many symmetries, that can be thought as a dynamical equivalent of
the torus in higher genera.

Together with L. Marchese and C. Ulcigrai, we show that for such
surfaces, similarly to what happens in the classical case, the Lagrange
spectrum contains an infinite interval, called Hall ray. In our
construction we use coding of hyperbolic geodesics and we deduce a
formula that allows to describe high values in the spectrum as a sum of
two Cantor sets.

Time permitting, we will also talk about an ongoing project about a
specific class of examples of Veech surfaces: the surfaces obtained by
gluing a regular 2n-gon. In this case one can prove finer result, for
instance studying the minimum of the spectrum, the so-called Hurwitz
constant.


VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)