Lecturer - University of Glasgow
I am a lecturer in pure mathematics at the University of Glasgow.
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.
My work lies in the intersection of algebraic topology, geometric topology, and geometric group theory. I am interested in developing new topological methods to study groups, algebras, and low dimensional manifolds. Some topics I'm interested in are moduli spaces of low dimensional manifolds (specifically links and 3-manifolds), Artin and Coxeter groups and monoids, and topological invariants of diagram algebras.
I am on the advisory board for 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.
Gabriel Corrigan, 2023-, joint supervision with Tara Brendle.
Sean O'Brien, 2024-, joint supervision with Jim Belk.
Susanna Terron, 2024-, joint supervision with Mike Whittaker.
If you are interested in applying for a PhD under my supervision please apply through the Centre for Doctoral Training in Algebra, Geometry and Quantum Fields. It is not necessary to email me beforehand. Students who apply to AGQ will also be eligible for other University of Glasgow Scholarships, so it is not necessary to apply separately.
I am a local organiser for the Scottish Topology Seminar.
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.
This year I am organising reading groups on Kirby Calculus and Operads at Glasgow.
January 2024: MFO mini-workshop on Artin Groups meet Triangulated Categories, co-organised with Edmund Heng and Viktoriya Ozornova.
26 April 2024: Topology of Artin groups, funded by a London Mathematical Society Celebrating New Appointments grant.
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
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)
A Deligne complex for Artin monoids, joint work with Ruth Charney and Rose Morris-Wright: Journal of Algebra, Volume 607:B (2022) 53-78. (arXiv:2007.12156)
The homology of the Brauer algebras, joint work with Richard Hepworth and Peter Patzt: Selecta Mathematica, New Ser. 27, 85 (2021). (arXiv:2009.11590)
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.
To prepare participants for the MFO mini-workshop Artin Groups meet Triangulated Categories, 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.
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.
Focus Program on Algebraic Topology In memory of Fred Cohen: July 2025 (dates tbc)
UK Topology in Low Dimensions Event (TILDE): 7-9 April 2025
Queen's University Belfast, Mathematical Sciences Research Centre colloquium: 31 March 2025
Durham University, Pure Maths Colloquium: 10 February 2025
Kyoto University, KTGU Special Lectures: 20-31 January 2025
INI Retreat: 9-13 December 2024
KCL Geometry seminar: 3 December 2024
AIM SQuaRE: 4-8 November 2024
Tufts Geometric Group Theory and Topology seminar: 29 October 2024
Columbia University Algebraic Topology seminar: 25 October 2024
British Topology Meeting: 28-30 August 2024
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 (talking in MS-19 and MS-58): 15 - 19 July 2024
GGSE - Oxford: 21 June 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
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.