Date/Time : 05 Nov 2025 15:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Ander Lamaison, Institute for Basic Science, South Korea

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.

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Date/Time : 05 Nov 2025 17:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Linus Richter, National University of Singapore

I prove two theorems which classify the complexity of certain sets of Borel codes. These are especially useful in the recursive construction of sets of reals in which Borel codes take on the role of “requirements”; our theorems show that certain classical constructions of sets of reals cannot be straightforwardly effectivised.

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