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.