Theons and quasirandomness

Abstract: There are two known approaches to the theory of limits of discrete combinatorial objects: geometric (graph limits) and algebraic (flag algebras). In the first part of the talk we present a general framework intending to combine useful features of both theories and compare it with previous attempts of this kind. Our main objects are $T$-ons, for a universal relational first-order theory $T$; they generalize many previously considered partial cases, some of them (like permutons) in a non-trivial way.

In the second part we apply this framework to offer a new perspective on quasi-randomness for combinatorial objects more complicated than ordinary graphs. Our quasi-randomness properties are natural in the sense that they do not use ad hoc densities and they are preserved under the operation of defining combinatorial structures of one kind from structures of a different kind. One key concept in this theory is that of unique coupleability roughly meaning that any alignment of two objects on the same ground set should ``look like'' random.

Based on joint work with Leonardo Coregliano.

combinatorics

Audience: researchers in the topic

Comments: Note the unusual time!

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Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.

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