Algebra seminar - Marianne Johnson
| Dates: | 5 March 2024 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Marianne Johnson |
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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
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
