Submonoid membership problems in one-relator groups and monoids, surface groups, and beyond

Abstract: The word problem for one-relator monoids remains one of the long-standing open questions in combinatorial algebra. One way to approach it is by studying related decision problems, in particular the submonoid membership problem, in both monoids and groups. In this talk, I will discuss how these problems are connected, drawing on classical work by Adian and Guba. I will also highlight the role of embeddings of right-angled Artin groups and trace monoids, which offer useful insights into the structure of these questions. Finally, I will present recent joint results with Robert D. Gray on the submonoid membership problem in surface groups, and in the broader hyperbolic setting.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper )

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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