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Spectral Rigidity of q-differential Metrics

Banff International Research Station for Mathematical Innovation and Discovery

When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask which curvesâ lengths do we really need to know It is a classical result of Fricke that a hyperbolic metric on a surface is determined by its marked simple length spectrum. More recently, DuchinâLeiningerâRafi proved that a flat metric induced by a unit-norm quadratic differential is also determined by its marked simple length spectrum. In this talk, I will describe a generalization of the notion of simple curves to that of q-simple curves, for any positive integer q, and show that the lengths of q-simple curves suffice to determine a non-positively curved Euclidean cone metric induced by a q-differential metric.

Mathematics; Dynamical systems and ergodic theory; Algebraic geometry; Dynamical systems

video/mp4

Author affiliation: University of Illinois at Urbana-Champaign

2019-11-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72455

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/