A glimpse into the asymptotics of polynomial identities

Many daily phenomena can be modelled by algebraic structures such as algebras. But what do the ‘rough shapes’ of these abstract objects look like? Commutativity, associativity, nilpotency,... all these important properties can be expressed in polynomials with non-commutative variables. At the 2016 BeNeLux Mathematical Congress the KWG Prize was awarded to Geoffrey Janssens. In this article he writes about his research on algebras satisfying polynomial identities and how they may be distinguished using asymptotic theory.