Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Tziotziou Natalia
Supervisors info:
Απόστολος Γιαννόπουλος, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Παντελής Δοδός, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Αριστείδης Κατάβολος, Ομότιμος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Η Εικασία του Hadwiger
Translated title:
Hadwiger's Conjecture
Summary:
We study a classical problem of discrete geometry, known as Hadwiger's
covering problem, asking for the smallest positive integer N with the
property that every n-dimensional convex body can be covered by the union
of at most N translates of its interior. Until recently, the best known
bounds were due to C. A. Rogers. Recently, a connection of the problem
with some well-known questions in asymptotic geometric analysis (the
thin-sell conjecture and the hyperplane conjecture) was discovered, and
this connection combined with recent developments in the above problems
has led to an improvement of the bounds of Rogers, although Hadwiger's
original question remains open. In this thesis we present the history of
the problem and all the known estimates until today.
Main subject category:
Science
Keywords:
Convex body, packing and covering numbers, logarithmically concave probability measures, isotropic constant, Hadwiger's conjecture.
Number of references:
107
