Minimal denominators and statistics of saddle connections of translation surfaces

YMSC Topology Seminar

Organizers：

陈伟彦、高鸿灏、黄意、林剑锋

Speaker：

Albert ARTILES (YMSC)

Time：

Thur., 4:00-5:00 pm, Sept. 26, 2024

Venue：

B725, Shuangqing Complex Building A

清华大学双清综合楼A座B725

Online：

Zoom Meeting ID: 405 416 0815

Passcode: 111111

Title：

Minimal denominators and statistics of saddle connections of translation surfaces

Abstract:

This talk will explore the connection between Diophantine approximations and the theory of homogeneous dynamics. The first part of the talk will be used to explicitly described the limiting distribution of the minimal denominator function, defined by

q_min(x,δ) = min{ q∈N : there exists p∈Z such that p/q∈(x−δ, x+δ)},

when the parameter δ tends to zero through the language of flows on the space of unimodular lattices.

The second part will be used to study the statistics of saddle connections of translation surfaces, with an emphasis on Veech surfaces.