Abstract
On the geometry of uniform meandric systems
Jacopo Borga
Stanford University
In 1912, Henri Poincaré asked the following simple question: “In how many different ways can a simple loop in the plane, called a meander, cross a line a specified number of times?”
Despite many efforts, this question remains open after over a century.
In this talk, I will focus on meandric systems, which are coupled collections of meanders.
I will present (1) a conjecture which describes the large-scale geometry of a uniform meandric system and (2) several rigorous results which are consistent with this conjecture.
Based on joint work with Ewain Gwynne and Minjae Park.
Despite many efforts, this question remains open after over a century.
In this talk, I will focus on meandric systems, which are coupled collections of meanders.
I will present (1) a conjecture which describes the large-scale geometry of a uniform meandric system and (2) several rigorous results which are consistent with this conjecture.
Based on joint work with Ewain Gwynne and Minjae Park.