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Summer School 2018 - Teichmüller dynamics, mapping class groups and applications.

Collection Summer School 2018 - Teichmüller dynamics, mapping class groups and applications.

Organizer(s) Pierre Dehornoy, Erwan Lanneau
Date(s) 11/06/2018 - 29/06/2018
linked URL https://if-summer2018.sciencesconf.org/
00:00:00 / 00:00:00
34 50

Marked points in genus two and beyond

By Paul Apisa

In the principal stratum in genus two, McMullen observed that something odd happens - there is only one nonarithmetic Teichmuller curve - the one generated by the decagon. This strange phenomenon begets another - a primitive translation surface in genus two admits a periodic point that is not a Weierstrass point or zero only if it belongs to the golden eigenform locus. In this talk, we will explain how to leverage results of Mirzakhani-Wright to study the orbit closures of translation surfaces with marked points and sketch a proof of the previously mentioned result in genus two. We will also explain how the result in genus two proves another uniqueness results - that there is at most one nonarithmetic rank two orbit closure in the minimal stratum in genus four - the one discovered by Eskin-McMullen-Mukamel-Wright.

Information about the video

  • Date of recording 27/06/2018
  • Date of publication 27/02/2026
  • Institution Institut Fourier
  • Licence CC BY NC ND
  • Language English
  • Format MP4

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