Conférence
Notice
Langue :
Anglais
Crédits
Fanny Bastien (Réalisation), Paul Apisa (Intervention)
Conditions d'utilisation
CC BY-NC-ND 4.0
DOI : 10.60527/z54r-jp63
Citer cette ressource :
Paul Apisa. I_Fourier. (2018, 27 juin). P. Apisa - Marked points in genus two and beyond , in 2018. [Vidéo]. Canal-U. https://doi.org/10.60527/z54r-jp63. (Consultée le 19 mars 2024)

P. Apisa - Marked points in genus two and beyond

Réalisation : 27 juin 2018 - Mise en ligne : 6 juillet 2018
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Descriptif

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.

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