CanaDAM 2021 En ligne, 25 - 28 mai 2021 canadam.math.ca/2021f
 english accueil réunion accueil canadam

Conférence grand public

GIL KALAI, Einstein Institute of Mathematics, Hebrew University
The beautiful combinatorics of convex polytopes  [PDF]

Convex polytopes attracted human attention since ancient times. Euler's formula, $\bf V-E+F=2$, for the numbers of vertices $\bf V$, edges $\bf E$, and faces $\bf F$ of a spacial polytope, is among the most important landmarks of mathematics, and it is a starting point for a rich theory of face numbers of polytopes in high dimensions. In the lecture I will present some major combinatorial results about polytopes, some connections to other areas of mathematics, pure and applied, a few mysterious phenomena, and some fascinating open problems.