Differential equations and geometry
Channel: Marcus Berg
Date: 2017-10-18

Riemann's ODE and hypergeometric functions. Stereographic projection of the Riemann sphere to the plane. Möbius invariance. Cross-ratio. Poincaré disk and upper half-plane. Examples ("Taxonomy"): spherical harmonics, Jacobi polynomials, Wigner's d-matrix, Bessel functions, Hermite functions, Laguerre functions, Error function, Polygamma function, Polylogarithm, Riemann zeta function. Anti-de Sitter space and the "hyperbolic cow approximation" (https://www.sns.ias.edu/~malda/Published.pdf)