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Algebra seminar - Marianne Johnson

Dates:5 March 2024
Times:14:00 - 15:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Current University students
Speaker:Marianne Johnson
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  • Department of Mathematics

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  • In category "Seminar"
  • In group "(Maths) Algebra"
  • By Department of Mathematics

Title: Tropical representations and semigroup identities of plactic-like monoids

Abstract: This talk concerns several well-studied families of monoids whose elements are combinatorial gadgets of a particular type over a fixed finite alphabet, and whose multiplication can be defined by means of an insertion algorithm. The prototypical example is the family of finite rank plactic monoids: these are infinite monoids arising from a natural combinatorial multiplication (determined by Schensted’s insertion algorithm) on semistandard tableaux over a fixed finite alphabet. The finite rank plactic monoids, and many finite rank 'plactic-like' monoids, can be faithfully represented by matrices over the tropical semiring; we construct such representations and utilise these to study semigroup identities satisfied by the finite rank plactic (joint work with Kambites) and plactic-like (joint work with Cain, Kambites and Malheiro) monoids.

Speaker

Marianne Johnson

Organisation: University of Manchester

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Simon Crawford

simon.crawford@manchester.ac.uk

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