Thesis supervisor: Károly Bezdek
Location of studies (in Hungarian): Pannon Egyetem, Műszaki Informatikai Kar, Matematika Tanszék Abbreviation of location of studies: PE
Description of the research topic:
One can briefly describe discrete geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. The goal of this research is to study some selected open problems in discrete geometry and their applications.
A molecule is a union of finitely many d-dimensional balls in Ed. Investigate isoperimetric-type problems of molecules and in particular, the long-standing Kneser-Poulsen conjecture ([1], [2]) according to which the volume of a d-dimensional molecule under an arbitrary contraction of its center points decreases in Ed for all d > 2. (This result was proved in [3] for d = 2.)
A kutatási téma előzményei:
[1] K. Bezdek, Classical Topics in Discrete Geometry, CMS Books in Mathematics, Springer, New York, 2010.
[2] K. Bezdek, Lectures on Sphere Arrangements - the Discrete Geometric Side, Fields Institute Monographs 32, Springer, New York, 2013.
[3] K. Bezdek and R. Connelly, Pushing disks apart - the Kneser-Poulsen conjecture in the plane, J. Reine Angew. Math. 553 (2002), 221-236.
Number of students who can be accepted: 1
Deadline for application: 2022-01-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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