Virtual Seminar on

Geometry and Topology

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Zoom Meeting ID 739-035-2844

Password Zero minus the Euler characteristic of a closed oriented surface of genus 4000

Time Wed 4 pm or Thursday 9 am (or so) in KST (Korea Standard Time)

2021

February 3 (W), 2021

10:00am - 11:30pm in Korean time

Inhyeok Choi (KAIST)

Simple length spectra of a generic hyperbolic surface determine its isometry class

Gel'fand asked in 1962 to which extent a closed hyperbolic surface is determined by its length spectrum. Strikingly, the examples of Vignéras and Sunada show that not all surfaces are determined by their length spectra. However, Wolpert proved that 'generic' closed hyperbolic surfaces are determined. Meanwhile, the analogous question with the simple length spectra has not been answered so far. Motivated by the technique of McShane and Parlier, we prove a variant of Wolpert's theorem involving the simple length spectra. To achieve this, we observe a rigidity of length identities over the Teichmüller space, which reads off subsurfaces of low complexity. In this talk, we explain this rigidity and discuss why our argument also applies to infinite-type surfaces. This is joint work with Hyungryul Baik and Dongryul M. Kim.



Organizers

Harry Hyungryul Baik (KAIST)

Sam Sang-hyun Kim (KIAS)

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