Recorded 23 May 2024. Jacopo Borga of Stanford University presents "On the geometry of uniform meandric systems" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop. Abstract: 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. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iv-vertex-models-algebraic-and-probabilistic-aspects-of-universality/