Date:
Wed, 03/12/202511:00-13:00
Zoom link: https://huji.zoom.us/j/88626455562?pwd=SPWmDh6phC7IzGmByi2YLZEamOlS3I.1
Meeting ID: 886 2645 5562
Passcode: 161334
Title: Higher-arity dividing lines and hypergraph regularity
Abstract: In recent years, the intersection of model theory and combinatorics has been a fertile ground for research. One notable example concerns the Szemerédi regularity lemma, a pivotal result in combinatorics that allows graphs to be decomposed into a bounded number of mostly uniform parts. Model-theorists have shown that if the graph is definable in a structure with suitable properties ('dividing lines') — NIP, stability, or distality — then it satisfies improved versions of the Szemerédi regularity lemma.
It often happens in maths that some theory is first developed in two dimensions, and finding the correct generalisation to n dimensions is as hard as doing so for 3 dimensions. This is well exemplified in the history of hypergraph regularity lemmas, and in the first part of the talk, we highlight some crucial features of their development. The same theme appears in the development of higher-arity generalisations of NIP, stability, and distality; these, along with their connections to hypergraph regularity lemmas, will be the subject of the second half of the talk. We will spend most of our time on higher-arity distality, with a focus on the higher-arity strong honest definitions we develop to prove an associated hypergraph regularity lemma.
Meeting ID: 886 2645 5562
Passcode: 161334
Title: Higher-arity dividing lines and hypergraph regularity
Abstract: In recent years, the intersection of model theory and combinatorics has been a fertile ground for research. One notable example concerns the Szemerédi regularity lemma, a pivotal result in combinatorics that allows graphs to be decomposed into a bounded number of mostly uniform parts. Model-theorists have shown that if the graph is definable in a structure with suitable properties ('dividing lines') — NIP, stability, or distality — then it satisfies improved versions of the Szemerédi regularity lemma.
It often happens in maths that some theory is first developed in two dimensions, and finding the correct generalisation to n dimensions is as hard as doing so for 3 dimensions. This is well exemplified in the history of hypergraph regularity lemmas, and in the first part of the talk, we highlight some crucial features of their development. The same theme appears in the development of higher-arity generalisations of NIP, stability, and distality; these, along with their connections to hypergraph regularity lemmas, will be the subject of the second half of the talk. We will spend most of our time on higher-arity distality, with a focus on the higher-arity strong honest definitions we develop to prove an associated hypergraph regularity lemma.