Rachael Boyd

Lecturer - University of Glasgow

About

In January 2023 I moved to the University of Glasgow as a lecturer.

Previous to this I was an EPSRC postdoctoral fellow in Cambridge, a postdoctoral research associate in Cambridge (in the group of Oscar Randal-Williams), a postdoc at the MPIM in Bonn, and an Alain Bensoussan ERCIM postdoc at the Norwegian University of Science and Technology. I completed my PhD at the University of Aberdeen in 2018, under the supervision of Richard Hepworth.

I am interested in developing new methods to study algebraic objects through the lenses of geometry and topology. Some topics I'm interested in are Artin and Coxeter groups and monoids, classifying spaces of groups and group homology, topological invariants of diagram algebras and corresponding applications to low-dimensional topology, and low-dimensional manifolds and embedding spaces. The majority of my work consists of building geometric models to study groups and algebras, such as semi-simplicial spaces, cube complexes and embedding spaces.

I am on the advisory board for the proto-academy phase of the Academy for the Mathematical Sciences, in the Early Career Mathematicians stream.

Contact

email: rachael.boyd@glasgow.ac.uk

address: Room 209D, School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow, G12 8QQ, United Kingdom.

Organising

On 26 April I am organising a meeting Topology of Artin groups, funded by a London Mathematical Society Celebrating New Appointments grant.

I am a local organiser for the Scottish Topology Seminar.

This year I am co-organising a reading group on Mapping class groups of 3-manifolds, with Mark Powell.

In January 2024 I co-organised a MFO mini-workshop on Artin Groups meet Triangulated Categories with Edmund Heng and Viktoriya Ozornova. To prepare participants for the workshop, I wrote some introductory notes on the geometric and combinatorial group theory of Artin groups, and Edmund wrote some introductory notes on stability conditions in triangulated categories.

In May 2025 I am co-organising a summer school on Homological aspects of groups and their classifying spaces, at the SwissMAP Research Station (SRS), with Macarena Arenas, Michel Bucher, and Nathalie Wahl.

Preprints

Moduli spaces of 3-manifolds with boundary are finite, joint work with Corey Bregman and Jan Steinebrunner - arXiv:2404.12748

Embedding spaces of split links, joint work with Corey Bregman - arXiv:2207.00619

Published papers

On the homology of the Temperley-Lieb algebras, joint work with Richard Hepworth: Geometry & Topology, 28:3 (2024) 1437–1499. (arXiv:2006.04256)

The Artin monoid Cayley graph, joint work with Ruth Charney, Rose Morris-Wright, and Sarah Rees: Journal of Combinatorial Algebra (2024), published online first https://doi.org/10.4171/jca/85. (arXiv:2303.09504)

The homology of the partition algebras, joint work with Richard Hepworth and Peter Patzt: Pacific Journal of Mathematics, 327(1):1–27, 2023.(arXiv:2303.07979)

The minimal genus problem for right angled Artin groups, joint work with Thorben Kastenholz and Jean Pierre Mutanguha: Geometriae Dedicata, 217, 93 (2023). (arXiv:2108.02914)

The homology of the Brauer algebras, joint work with Richard Hepworth and Peter Patzt: Selecta Mathematica, New Ser. 27, 85 (2021). (arXiv:2009.11590)

A Deligne complex for Artin monoids, joint work with Ruth Charney and Rose Morris-Wright: Journal of Algebra, https://doi.org/10.1016/j.jalgebra.2021.03.015, 2021. (arXiv:2007.12156)

Combinatorics of injective words for Temperley-Lieb algebras, joint work with Richard Hepworth: Journal of Combinatorial Theory, Series A , 181:105446, 2021. (arXiv:2006.04261)

Homological stability for Artin monoids: Proceedings of the London Mathematical Society, 121(3):537–583, 2020. (arXiv:1808.07722)

The low dimensional homology of finite rank Coxeter groups: Algebraic & Geometric Topology, 20-5 (2020), 2609--2655. (arXiv:1811.00400) Erratum.

My thesis was titled Homology of Coxeter and Artin groups and can be viewed here. The code for the thesis uses PyCox, please email me if you would like to see it.