In the lecture I will describe some combinatorial problems concerning
convex sets and convex polytopes. Some such connections are quite old.
Examples are: The classification of Platonic solids; Euler's famous
formula V-E+F =2; Helly's theorem that asserts that given n convex sets in d-space, if every d+1 of those convex sets share a point then all of them do. And there are
splendid new examples and related problems that we will discuss in the lecture. The lecture will be quite elementary and students are welcomed.
Gil Kalai studoval na Hebrew University v Jeruzaleme (Ph.D. pod vedenim M.A.Perlese), kde je
dnes radnym profesorem matematiky (Henry and Manya Noskwith chair). Je rovnez profesorem matematiky a
informatiky na Yale University. Hlavni oblasti zajmu profesora Kalaie je kombinatorika a konvexni
geometrie v sirokem matematickem a informatickem kontextu: teorie konvexnich mnohostenu, souvislosti
kombinatoriky s topologii a Fourierovou analyzou, booleovske funkce, prahove a isoperimetricke problemy.
Venuje se rovnez aplikacim kombinatoriky v teoreticke informatice, optimalizaci, pravdepodobnosti a
ekonomii. G. Kalai je prednim svetovym odbornikem. Prednesl zvanou prednasku na Svetovem kongresu
matematiku v Zurichu a jako jeden z mala matematiku ziskal vsechny mezinarodni ceny udelovane
v kombinatorice, diskretni matematice a optimalizaci: Polyovu cenu (1992), Erdosovu cenu (1993)
a Fulkersonovu cenu (1994). Prednasky Gila Kalaie jsou proslule. Jeho kolokvium je urceno
nejsirsi matematicke a informaticke verejnosti.