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Details of talk

TitleCongruence lattices in diagram monoids
PresenterJames East (University of Western Sydney)
Author(s)Dr James East
Time17:00:00 2016-12-06

A congruence on a semigroup is an equivalence relation that is compatible with
the semigroup operation.  Congruences play a role in semigroup theory akin to
normal subgroups in group theory: congruences are the appropriate way to define
kernels of semigroup homomorphisms, and they govern the formation of quotient
semigroups.  The set of all congruences of a semigroup forms a (complete
algebraic) lattice under inclusion.  In this talk, I'll review some known
results on congruence lattices, and then report on recent work with James
Mitchell, Nik Ru\v{s}kuc and Michael Torpey (St Andrews) in which we completely
describe the congruence lattices of the finite partition, Brauer and
Temperley-Lieb monoids, and a few others.