Unit: MTA-ELTE Lendület Combinatorial Geometry (CoGe) Research Group
Place: 1117 Budapest, Pázmány Péter sétány 1/C
Main tasks and responsibilities: The primary task of the trainee will be to write computer codes for problems in combinatorial geometry.
Working hours: 20 hours/week
Colouring geometric hyper-graphs is the main topic of our research, with several projects running currently with different students. An interesting recent result is that the Delaunay-graph defined by one pseudo-disk family on another pseudo-disk family is always planar. The other main topic of the group is to determine the chromatic number of the plane, known as the Hadwiger–Nelson problem. Related to this, we have improved the best bound for the number of unit distances from 8n^(4/3) to 2,1n^(4/3). We also proved results related to the intersection number of two polygons; areas of triangles determined by n lines; context-free languages; Berge–Ramsey problems; Gallai colourings of graphs.