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)