Counting pairs of saddle connections on translations surfaces | Vidéo | Carmin.tv

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Counting pairs of saddle connections on translations surfaces

By Howard Masur

saddle connections

Appears in collection : Combinatorics, Dynamics and Geometry on Moduli Spaces / Combinatoire, dynamique et géométrie dans les espaces de modules

In this talk I will consider the problem of counting the number of pairs (z,w) of saddle connections on a translation surface whose holonomy vectors have bounded virtual area. That is, we fix a positive A and require that the absolute value of the cross product of the holonomy vectors of z and w is bounded by A. One motivation is the result of Smillie-Weiss that for a lattice surface there is a constant A such that if z and w have virtual area bounded by A then they are parallel. We show that for any A there is a constant $c_A$ such that for almost every translation surface the number of pairs with virtual area bounded by A and of length at most R is asymptotic to $c_AR^2$ as R goes to infinity. This is joint work with Jayadev Athreya and Samantha Fairchild.

Information about the video

Date of recording 20/09/2022
Date of publication 07/10/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19960603
Cite this video Masur, Howard (20/09/2022). Counting pairs of saddle connections on translations surfaces. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19960603
URL https://dx.doi.org/10.24350/CIRM.V.19960603

Domain(s)

Dynamical Systems

Bibliography

ATHREYA, J. S., FAIRCHILD, Samantha, et MASUR, Howard. Counting pairs of saddle connections. arXiv preprint arXiv:2201.08628, 2022. - https://arxiv.org/abs/2201.08628

MSC codes

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