De 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.
De Pascal Hubert
De Pascal Hubert
De Christopher Leininger
De Alex Wright
De Anna Lenzhen
De Christopher Leininger
De Christopher Leininger
De Sasha Skripchenko
De Sasha Skripchenko
De Rodolfo Gutierrez
De Anton Zorich
De Anton Zorich
De Anton Zorich
De Vaibhav Gadre
De Irene Pasquinelli
De Olga Paris-Romaskevich
