The Rogers-Ramanujan Identities and the Icosahedron - Lecture 3
Offered By: ICTP Mathematics via YouTube
Course Description
Overview
Explore the fascinating world of Rogers-Ramanujan identities and their connection to the icosahedron in this comprehensive lecture. Delve into the unexpected appearance of the number "5" in both these identities and the theory of Platonic solids. Discover the intricate relationships between pure number theory, modular forms, combinatorics, continued fractions, conformal field theory, and mirror symmetry. Gain insights into various mathematical gems, including Apéry's proof of the irrationality of ζ(2). Follow along as the lecturer covers topics such as definitions, proofs, least common multiples, L-series, and more, in a manner accessible to mathematicians of all levels and backgrounds.
Syllabus
Intro
Recap
Definitions
Breeze proof
Oneline proof
Ugly cancellation miracle
Least common multiple
Pears proof
Art of T
General Theorem
Example
Lseries
Proof
Miscellaneous
Taught by
ICTP Mathematics
Related Courses
3D Gravity and Teichmueller TQFT - Lorenz EberhardtKavli Institute for Theoretical Physics via YouTube Generalized Narain VOAs and Ensemble Averages from Real Analytic Eisenstein Series
Galileo Galilei Institute via YouTube AdS/CFT Correspondence for Scalar Field Theory in Lattice AdS_2 and AdS_3
Advanced Cyberinfrastructure Training at RPI via YouTube Schramm Loewner Evolution and Lattice Models - Advanced Course Lecture 1, Part 1
Fields Institute via YouTube Advanced Course I: Schramm Loewner Evolution and Lattice Models - Lecture 2, Part 2
Fields Institute via YouTube