# Pure Maths Colloquium: Norá Szakács

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

 Where: Lecture Theatre C When: Apr 4 2019 @ 16.00 Video: Not recorded
 Speaker: Norá Szakács University of York Title: Algorithmic properties of tree-like inverse monoids

Inverse monoids are monoids equipped with an involutive inverse operation that satisfies the identities $$mm^{-1}m=m$$ and $$mm^{-1}nn^{-1}=nn^{-1}mm^{-1}$$. They can be considered as the abstractions of partial symmetries, and are one of the many generalizations of groups. The Cayley graph of an inverse monoid need not be strongly connected, nevertheless, the strongly connected components, called Schützenberger graphs, form metric spaces. We prove that if a finitely presented inverse monoid has tree-like Schützenberger graphs, then the Schützenberger graphs have regular geodesics, and the inverse monoid has a solvable word problem.