The seminars in Discrete Mathematics are aimed at researchers, employees, and students.
This week's seminar is given by Ander Lamaison, Institute for Basic Science, Daejeon, South Korea.
Title: Palettes determine uniform Turán density
Abstract: We study Turán problems for hypergraphs with an additional uniformity condition on the edge distribution. This kind of Turán problems was introduced by Erdős and Sós in the 1980s but it took more than 30 years until the first non-trivial exact results were obtained. Central to the study of the uniform Turán density of hypergraphs are palette constructions, which were implicitly introduced by Rödl in the 1980s. We prove that palette constructions always yield tight lower bounds, unconditionally confirming present empirical evidence. This results in new and simpler approaches to determining uniform Turán densities, which completely bypass the use of the hypergraph regularity method.
