Generalized BCZ-maps are weakly mixing

Speaker: Albert Alejandro Calix Artiles (YMSC)

Time: 2025-12-12, 12:00-13:00 (Cancelled)
Location: 1010, SIMIS
Zoom Meeting ID: 878 7041 1316 Passcode: SIMIS

摘要：

In 2001, Boca-Cobeli-Zaharescu introduced what is now known as the BCZ map in order to resolve a conjecture of Hall. About a decade later, Athreya-Cheung independently rediscovered the map while studying horocycle excursions to the cusp in the space of unimodular lattices. Using tools from homogeneous dynamics, they established that the BCZ map is ergodic and has zero entropy. Since then, the BCZ map has been generalized to the setting of translation surfaces. The first part of this talk will be devoted to describing this generalization.
In 2024, Cheung–Quas proved that the classical BCZ map is weakly mixing. In the second part of the talk, we will discuss how their argument can be adapted to the generalized BCZ maps arising from SL(2, R)-orbits of Veech surfaces. To accomplish this, we introduce a version of the Siegel-Veech transform conditioned on horizontally short saddle connections and analyze its statistical properties.