Description:

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 the first part of the mini-course, I will present the conjectural scaling limit of uniform meanders and discuss some of its curious properties (both at the discrete and continuum levels). The second part will examine a related model called meandric systems. A meandric system is a coupled collection of meanders. Also, in this case, I will present a conjecture describing the large-scale geometry of a uniform meandric system and several rigorous results consistent with this conjecture.

**Lecture times:**

(1) Wednesday, April 3rd, 2024, 2:00-3:30 PM [**Location: **Fields Institute, Room 230, Toronto]

(2) Friday, April 5th, 2024, 2:00-3:30 PM [Location: Fields Institute, Room 230, Toronto]

(3) Wednesday, April 10th, 2024, 3:00-4:30 PM [Location: Fields Institute, Room 230, Toronto]

(4) Friday, April 12th, 2024, 3:00-4:30 PM [Location: Fields Institute, Room 230, Toronto]

**Zoom link:** https://zoom.us/j/97241819130

**Instructor:** Jacopo Borga, jborga_at_stanford.edu.

**Lecture notes:**

Meanders_and_Meandric_Systems-Lecture-1 (PDF)

Meanders_and_Meandric_Systems-Lectures-2-and-3 (PDF)

Meanders_and_Meandric_Systems-Lecture-4 (PDF)