On the upper bound of the geotopological Cheeger constant in the principal stratum
Date(s) : 29/09/2023 iCal
11h00 - 12h00
On the upper bound of the geotopological Cheeger constant in the principal stratum
Abstract:
We are exploring the behavior of a topological variant of the Cheeger constant on principal strata $left(mathcal{H}left(1^{2g-2}right)right)_g$ of translation surfaces as genus $g$ approaches infinity. Our goal is to derive a more comprehensive understanding of the expected value of this constant and its rate of growth.
Through our analysis, we demonstrate that the expected value of the topological variant of the Cheeger constant has an upper growth rate like $g^{3}$ for large genus $g$. In particular, we build on the results of Eskin–Masur–Zorich, which provide an explicit way of calculating volumes of subspaces of strata of Abelian differentials.
Emplacement
Saint-Charles - FRUMAM (2ème étage)
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