Rachael Boyd

POSTDOC - University of Cambridge


About

I am currently an EPSRC Postdoctoral Fellow at the University of Cambridge, working in the Department of Pure Mathematics and Mathematical Statistics in the group of Oscar Randal-Williams . I am also a Bye Fellow at Murray Edwards College. From January 2023 I'll be a lecturer at the University of Glasgow.


Previous to this I was a postdoc at the Max-Planck-Institut für Mathematik 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, 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 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.


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.



Preprints

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

The minimal genus problem for right angled Artin groups, joint work with Thorben Kastenholz and Jean Pierre Mutanguha - arXiv:2108.02914


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 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.


Recent and upcoming talks

Stockholm Univesity Algebra and Geometry seminar: 30 November 2022

Oxford Geometric Group Theory seminar: 15 November 2022

Copenhagen Topology seminar: 23 October 2022

Classifying spaces in homotopy theory, in honour of Ran Levi's 60th Birthday: 5-9 September 2022

NBGGT meeting at Heriot-Watt: 10 June 2022

LSU Topology seminar: 13 April 2022

MIT Geometry and Topology seminar: 11 April 2022

Braids in Symplectic and Algebraic Geometry: 21-25 March 2022 (travel allowing, my current plan is to spend April 2022 at ICERM)

Cambridge Geometric Group Theory seminar: 21 January 2022

Transpennine Topology Triangle 115: 17 December 2021

Cambridge Differential Geometry and Topology seminar: 17 November 2021

MPIM Topology seminar, talk one in the miniseries RAAG-Out: a savoury geometric group theory sampler : 10 May 2021

AMS special session on Categorical and Combinatorial Methods in Representation Theory, and Related Topics: 1-2 May 2021

IMUNAM Algebraic Topology Seminar: 29 April 2021

St Andrews University Mathematics Society Guest Lecture : 14 April 2021

Aberdeen Topology Seminar: 17 March 2021

TAPIRS - Talks About Progress In Representation Stability: 26 February 2021

Glasgow Topology Seminar: 1 February 2021


Teaching

Lent 2022: Coxeter groups. Meme competition.

Spring 2019: General Topology.


Links

This page contains links for studying [GMTW], which was our topic in the topology learning seminar at NTNU.

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.


Contact

email: rachaelboyd@dpmms.cam.ac.uk

address: DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK