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Sunflowers and Ramsey problems for restricted intersections

组织者

马杰 , 本杰明·苏达科夫

演讲者

Barnabas Janzer

时间

2026年03月10日 17:05 至 18:15

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

Extremal problems on set systems with restricted intersections have been an important part of combinatorics in the last 70 years. For many of the known results, one of the fundamental tools used is Füredi’s celebrated semilattice lemma, which is a key ingredient in the powerful delta-system method. Motivated by a Ramsey-type problem for restricted intersections, we study the quantitative dependence in Füredi’s result, and prove that one cannot remove the double-exponential dependency on the uniformity. However, we provide an alternative with significantly better, single-exponential dependency on the parameters, which is still strong enough for most applications of the delta-system method. Joint work with Zhihan Jin, Benny Sudakov and Kewen Wu.