Event Detail

Event Type: 
Number Theory Seminar
Date/Time: 
Tuesday, March 1, 2022 - 10:00 to 11:00

Speaker Info

Institution: 
L'École normale supérieure - PSL
Abstract: 

In this presentation I will define the notion of connection point on a translation surface, which was used in particular P. Hubert and T.Schmidt to construct translation surfaces with infinitely generated Veech groups. After a quick review about translation surfaces and Veech groups, we will see that if those points are well characterized for translation surfaces of genus 2 and covers, this is not the case in higher genus, starting from genus 3. In this talk I will focus on the case of the double heptagon, a translation surface of genus 3, and explain how to relate connection points to Hecke continued fractions. This will allow in particular to show that central points of the double heptagon are not connection points, giving a negative answer to a question by P. Hubert and T. Schmidt.