Marked points in genus two and beyond

Bewegte Bilder

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.

Show object

• Location: Hannover TIB
• Extent: 688MB, 00:58:06:00 (unknown)
• Language: Englisch
• Notes: Audiovisuelles Material

References and Relationships

• Bibliographic citation: Summer School 2018 - Teichmüller dynamics, mapping class groups and applications ; (Jan. 2018)

Contributors, Places and Time

• Event: Veröffentlichung
• (who): Institut Fourier
• (when): 2018-01-01
• Contributor: Apisa, Paul ; Bastien, Fanny

Further information

• DOI: 10.5446/63382