## Algebra, Combinatorics, Measure

Organizers: Gabor Elek, Łukasz Grabowski, Tony Nixon

Contact: Ł.G.

Seminar is on **Mondays**, usually at 1PM in B35.

This is a research seminar with both internal and external speakers. Topics covered might include, but are by no means limited to, group rings of infinite groups, $l^2$-invariants, appoximations of infinite groups (for example sofic groups), asymptotic and measured group theory, graph rigidity, discrete geometry, Borel and measurable combinatorics, graph limits, interactions between algebra/combinatorics and operator algebras, probability, etc.

We have a mailing list: acmseminar@lists.lancs.ac.uk. In order to participate either ask ŁG to sign you up, or send a *plain text* email to majordomo@lists.lancs.ac.uk, containing only the two words `subscribe acmseminar`

in the body (you can leave the subject empty).

### 2017-18

### Abstracts

In Ramsey theory, Schur's theorem states that however one colours the positive integers with finitely many colours, there always exists a solution to the equation x+y = z in which each variable receives the same colour. Rado completely characterised which linear equations possess this property and which do not. We discuss analogues of these results for certain non-linear Diophantine equations.