The Rogers-Ramanujan Identities and the Icosahedron - Lecture 2

Explore the fascinating connections between the Rogers-Ramanujan identities and the icosahedron in this comprehensive lecture. Delve into a wide range of mathematical topics, including number theory, modular forms, combinatorics, continued fractions, conformal field theory, and mirror symmetry. Discover how the unexpected appearance of the number "5" links these seemingly disparate areas of mathematics. Examine the intricate relationships between pure number theory, the theory of modular forms, and the most complex Platonic solids. Investigate additional mathematical gems, such as Apéry's proof of the irrationality of ζ(2). Learn about the E8 lattice, stereographic projection, binary icosahedral groups, polytopes in n-space, and invariant theory. Gain insights into the application of these concepts to the mirror quintic theory of Candelas et al. Suitable for mathematicians of all levels and interests, this lecture provides an accessible survey of these interconnected mathematical marvels without requiring extensive prerequisites.

Introduction
The icosahedron
The e8 lattice
The e8 model
Stereographic projection
Binary icosahedral groups
Polytopes in nspace
Unitquaternions
E8 lattice
Invariant theory
Groups
Eigenstein series
Free identities