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Seminar za Logiku, Algebru, DIskretnu Matematiku i teorijsko računarstvo
Logic, Algebra, DIscrete Mathematics and Theoretical Computer Science Seminars

Školska 2024/25. / Academic year 2024/25

09/10/2024

Vladimir Tasić (University of New Brunswick, Fredericton, Canada): Brouwer-Weyl continuum throught 3D glasses: Geometry, computation, general relativity

Abstract (pdf)

26/09/2024

Robert D. Gray (University of East Anglia, Norwich, UK): The geometry of the word problem for groups and inverse monoids

The most fundamental algorithmic problem in algebra is the word problem, which asks whether there is an algorithm that takes two expressions over a set of generators and decides whether they represent the same element. Despite the huge advances that have been made in this area over the past century, there are still many basic questions about the word problem, and related algorithmic problems, for finitely presented groups and monoids that remain open.

Important work of Ivanov, Margolis, Meakin, and Stephen in the 1990s and 2000s shows how algorithmic problems for groups and monoids can be related to corresponding questions about finitely presented inverse monoids. This is a natural class that lies between groups and monoids, and corresponds to the abstract study of partial symmetries. There is a powerful range of geometric methods for studying inverse monoids such as the Scheiblich/Munn description of free inverse monoids and Stephen's procedure for constructing Schutzenberger graphs.

In this talk I'll explain these connections, and discuss recent advances in our understanding of the behaviour of the geometry of Cayley graphs of inverse monoids, and how this has been used to prove new and unexpected results about their algorithmic and algebraic properties.

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