Higher Genus Meanders and Masur-Veech Volumes

Explore the fascinating world of higher genus meanders and Masur-Veech volumes in this comprehensive conference talk. Delve into the concept of classical meanders and their exponential growth patterns before expanding to pairs of transversally intersecting simple closed curves on closed oriented surfaces of arbitrary genus. Discover the polynomial asymptotics of genus g meanders with n bigons and learn about the asymptotic probability of obtaining a meander from random braids on surfaces. Gain insights into the identification of meanders with integer points represented by square-tiled surfaces in moduli spaces of Abelian and quadratic differentials. Examine the application of recent advances in moduli space geometry and asymptotic properties of Witten-Kontsevich 2-correlators on moduli spaces of complex curves to effectively count meanders.