Topological Recursion: A Recursive Way of Counting Surfaces
Offered By: Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Course Description
Overview
Explore the fascinating world of surface enumeration in this 55-minute lecture by Bertrand Eynard from the Institut de physique théorique, CEA Saclay. Delve into the importance of counting various types of surfaces in combinatorics of maps, enumerative geometry, string theory, and statistical physics. Discover how the "topological recursion" provides a universal method for enumerating surfaces of higher genus and with more boundaries, starting from the enumeration of discs and cylinders. Learn about the beautiful mathematical properties of this recursion and its connections to other areas of mathematics and physics, including integrable systems and random matrices. Gain insights into the significance of surface enumeration problems, such as Mirzakhani's recursion for hyperbolic surfaces, and understand how topological recursion serves as a powerful tool in bridging different mathematical and physical concepts.
Syllabus
Bertrand Eynard - Topological Recursion: a recursive way of counting surfaces
Taught by
Institut des Hautes Etudes Scientifiques (IHES)
Related Courses
Физика как глобальный проектNational Research Nuclear University MEPhI via Coursera Advanced statistical physics
École Polytechnique Fédérale de Lausanne via edX Insights on Gradient-Based Algorithms in High-Dimensional Learning
Simons Institute via YouTube Statistical Physics and Computation in High Dimension
Simons Institute via YouTube Computing Partition Functions, Part I
Simons Institute via YouTube