Thesis supervisor: Jenő Szirmai
Location of studies (in Hungarian): Department of Geometry, Institute of Mathematics, BME Abbreviation of location of studies: BME
Description of the research topic:
The classical sphere packing problems concern arrangements of non-overlapping equal spheres (rather balls) which fill a space. Space is the usual three-dimensional Euclidean space. However, ball (sphere) packing problems can be generalized to the other
3-dimensional Thurston geometries
and to higher dimensional various spaces.
In an n-dimensional space of constant curvature d_n(r) be the density of n+1 spheres of radius r mutually touching one another with respect to the simplex spanned by the centres of the spheres. L. Fejes Tó'th and H.S.M. Coxeter conjectured that in an n-dimensional space of constant curvature the density of packing spheres of radius r can not exceed d_n(r).
This conjecture has been proved by C. Roger in the Euclidean space. The 2-dimensional case has been solved by L. Fejes Tóth. In an 3-dimensional space of constant curvature the problem has been investigated by Böröoczky and Florian and it has been studied by K. Böröczky for n-dimensional space of constant curvature (n> 3).
We have studied some new aspects of the horoball and hyperball packings in n-dimensional hyperbolic space and we have realized that the ball, horoball and hyperball packing problems are not settled yet in the n-dimensional n>2 hyperbolic space.
The goal of this PhD program to generalize the above problem of finding the densest geodesic and translation ball (or sphere) packing and covering to the other 3-dimensional homogeneous geometries (Thurston geometries) .
Moreover, we will study the structure of Dirichlet-Voronoi cells related to the packing configurations.
We note here that the greatest known packing density is realized in geometry with packing density is ~0.87499429 .
We will use the unified interpretation of the Thurston geometries in the projective 3-sphere.
Required language skills: English Number of students who can be accepted: 1
Deadline for application: 2017-05-31
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).
Login
