Discrete Math Seminar: Eric Fusy

  • Date: 03/17/2015
  • Time: 16:00
Eric Fusy, Ecole Polytechnique

University of British Columbia


Introduction to maps II: planar map enumeration


In the planar case a map can be seen as a connected graph embedded on the sphere (or in the plane) up to continuous deformation. The enumeration of (rooted) planar maps has started in the 60's with the seminal work of Tutte who found surprisingly simple counting formulas for several families of planar maps. We will briefly review on Tutte's method and present in details the more recent bijective approach, focusing on the Cori-Vauquelin-Schaeffer bijection for planar quadrangulations. This bijection has become famous since it makes it possible to trace the distances (from a distinguished vertex) in the map, and as such it has proven a fundamental tool in the recent proof that random planar quadrangulations (rescaled by n^{1/4}) converge to the so-called Brownian map.


This the second talk of a series of 3 talks, the 3rd one will focus on distance properties in random planar maps

Other Information: 

Location: ESB 4127