Incidences and Tilings in Linear Geometry

Explore the fascinating intersection of incidence geometry and surface tilings in this 57-minute lecture by Sergey Fomin from the University of Michigan. Delve into a groundbreaking "master theorem" that unifies classical theorems of real and complex linear incidence geometry, including those of Pappus, Desargues, and Möbius. Discover how this theorem relates to quadrilateral tilings of closed oriented surfaces, opening up new avenues for generating and generalizing incidence theorems. Gain insights into joint research with Pavlo Pylyavskyy, presented at IPAM's Statistical Mechanics and Discrete Geometry Workshop at UCLA on March 26, 2024.