ODT - THESIS TOPIC: János Barát: Intersecting hypergraphs, finite geometries


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Thesis topic proposal

Intersecting hypergraphs, finite geometries

THESIS TOPIC PROPOSAL

Institute: University of Szeged
mathematics and computing
Doctoral School of Mathematics

Thesis supervisor: János Barát
Location of studies (in Hungarian): Bolyai Institute, Faculty of Science and Informatics, University of Szeged, Hungary
Abbreviation of location of studies: MatDI

Description of the research topic:

In the case of intersecting hypergraphs, the sharp examples for several extremal questions come from finite projective planes. Let us assume that the hypergraph has no small cover. How many edges can it have? We can also consider the question only for finite projective planes. Are there intersecting hypergraphs in which the intersection of any two edges has at least 2 vertices? We can search for such hypergraphs using a computer.

Required language skills: English
Number of students who can be accepted: 1

Deadline for application: 2024-12-31