Pure maths colloquium - Bethany Marsh
| Dates: | 15 May 2026 |
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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: Bethany Marsh (University of Leeds)
Title: Additive friezes
Abstract: Joint work with Asilat Bapat, Véronique Bazier-Matte, Eleonore Faber, Kunda Kambaso and Yadir Valdivieso.
Shephard pointed out in 1976 that the addition table for the natural numbers, when drawn in the right way, has the property that each 2 by 2 submatrix has determinant 1, while the multiplication table has an analogous additive property. A Coxeter-Conway frieze consists of alternating rows of positive integers satisfying the former condition, so he indicated that it is natural to consider additive friezes satisfying the latter condition.
This talk will be an introduction to additive friezes. We show that they give rise to a polytope which can be regarded as a symmetrisation of a realisation of the associahedron, given by Arkani-Hamed, Bai, He and Yan and Bazier-Matte, Chapelier-Laget, Douville, Mousavand, Thomas and Y?ldir?m.
Additive friezes can be defined on any Auslander-Reiten quiver, and we show that additive friezes on the Auslander-Reiten quiver of the bounded derived category of a path algebra of a Dynkin quiver are periodic, generalising a result of Shephard in the classical case.
Room: Frank Adams 1
The talk will be followed by a reception.
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
