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Details of Grant 

EPSRC Reference: EP/S020616/1
Title: Diagram Monoids and Their Congruences
Principal Investigator: Ruskuc, Professor N
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics and Statistics
Organisation: University of St Andrews
Scheme: Overseas Travel Grants (OTGS)
Starts: 15 December 2018 Ends: 14 February 2021 Value (£): 35,035
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
Diagram monoids have over the last few years come into sharp focus, because of their fundamental role in the formation of diagram algebras, which in turn have applications in representation theory and theoretical physics, and also because of their intriguing algebraic and combinatorial properties. Until recently, investigations were largely concerned with the basic semigroup-theoretic and combinatorial properties of these monoids, for instance determination of Green's equivalences, computations of minimal generating sets and defining relations, and characterisations and counting of idempotents. PI (NR) and James East (JE) have recently started a collaboration on another important aspect of these monoids, namely their congruences. In a ground-breaking paper (joint with J.D. Mitchell and M. Torpey) they classified all the congruences on all classical diagram monoids over a finite set. In the process they started developing what looks like a promising general theory of semigroup congruences, at least for finite semigroups. Arising from this work are a number of strands, each important in its own right, and the project proposed here is designed to enable these strands to be followed up and for their full potential to be realised. We have identified four work packages -- dealing with infinite partition monoids, infinite diagram monoids, finite and infinite twisted diagram monoids, and development of a general theory of congruences -- which will be investigated in the course of four research visits by NR to JE over a period of two years.

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Organisation Website: http://www.st-and.ac.uk