Rachael Boyd

Lecturer - University of Glasgow


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.


email: rachael.boyd@glasgow.ac.uk

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


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.


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

Accepted papers

On the homology of the Temperley-Lieb algebras, joint work with Richard Hepworth: accepted for publication in Geometry & Topology. (arXiv:2006.04256)

Published papers

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.

Recent and upcoming talks and travel

Topology of moduli spaces, in honour of Ulrike Tillmann's 60th birthday: 19 - 24 August 2024

MFO Workshop - Topologie: 22 - 26 July 2024

European Congress of Mathematics: 15 - 19 July 2024

Dubrovnik X - Topology & Dynamical Systems: 24-28 June 2024

Modern methods in infinite groups, in honour of Ian Leary's 60th birthday: 12 - 14 June 2024

Topology, representation theory and higher structures: 27 May - 7 June 2024

Algebra Days in Caen 2024: Algebraic aspects of configuration spaces and moduli spaces: 18-20 March 2024

Scottish Topology Seminar: 4 March 2024

Lancaster Pure Maths seminar: 27 February 2024

MFO Mini-Workshop - Artin Groups meet Triangulated Categories (organiser): 28 January - 2 February 2024

Heriot Watt GGT seminar: 22 November 2023

Bristol Geometry and Topology seminar: 21 November 2023

Tufts Geometric Group Theory and Topology seminar: 19 September 2023

Geometry and topology of Artin groups, AIM : 11-15 September 2023

British Topology Meeting 2023: 6-8 September 2023

Workshop on Homology of Configuration Spaces and related topics: 15-17 May 2023

Women in Number Theory and Geometry Spring Retreat: 17-20 April 2023

Edinburgh Hodge seminar: 8 March 2023

Southampton topology seminar: 6 February 2023

Glasgow Geometry and Topology seminar: 16 January 2023


Semester 2 2023, 2024: Further topics in group theory. Glasgow students taking this course should see Moodle.

Lent 2022: Coxeter groups. Meme competition.

Spring 2019: General Topology.


Mapping class groups of 3-manifolds seminar, Glasgow, Autumn 2023.

Topology learning seminar on GMTW, NTNU, 2019.

Staying in the game - an essay by Daniel Nettle.

"I Hate Paintings." - a blog post by Robert Spencer, featuring an excerpt from “The Pocket Guide to Artistry in the 20th Century” by Sir A. R. Tiste.

Math-life balance - a series of interviews by Mura Yakerson.