Logic Seminar - Mervyn Tong
| Dates: | 18 February 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Mervyn Tong (University of Cambridge)
Higher-arity distality and hypergraph regularity
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. Chernikov and Starchenko showed that if the graph is definable in a distal structure, then it satisfies an improved version of the Szemerédi regularity lemma.
It often happens in maths that some theory is first developed in two dimensions, and finding the correct extension to n dimensions is as hard as doing so for 3 dimensions. This is well exemplified in the history of hypergraph regularity lemmas. We will give an overview of the key features and difficulties in finding a 3-uniform hypergraph extension of the Szemerédi regularity lemma, before discussing our extension of Chernikov and Starchenko's result to hypergraphs definable in structures satisfying a certain notion of higher-arity distality. We will highlight a key innovation required for the proof, namely, higher-arity strong honest definitions that we develop for this notion of higher-arity distality.
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Frank Adams 1
Alan Turing Building
Manchester
