Incidences and tilings

Sergey Fomin
University of Michigan

We show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a single "master theorem" that involves an arbitrary tiling of a closed oriented surface by quadrilateral tiles. This yields a general mechanism for producing new incidence theorems and generalizing the known ones. This is joint work with Pavlo Pylyavskyy.

Presentation (PDF File)

Back to Workshop I: Statistical Mechanics and Discrete Geometry