Algebra, Combinatorics, Measure
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, -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.
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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.