Rachael Boyd

POSTDOC - Max-Planck-Institut für Mathematik


(photo by Julia Semikina)

About

I am currently a postdoc at the Max-Planck-Institut für Mathematik in Bonn, Germany.


Previous to this I was an Alain Bensoussan ERCIM postdoc at the Norwegian University of Science and Technology, and I did 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

On the homology of the Temperley-Lieb algebras , joint work with Richard Hepworth - arXiv:2006.04256


Accepted papers

The homology of the Brauer algebras , joint work with Richard Hepworth and Peter Patzt: accepted for publication in Selecta Mathematica. (arXiv:2009.11590)


Puplished papers

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.


Upcoming talks

Glasgow Topology Seminar: 1 February 2021

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

Aberdeen Topology Seminar: 17 March 2021

St Andrews University Mathematics Society Guest Lecture : 14 April 2021

IMUNAM Algebraic Topology Seminar: 29 April 2021

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

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


Links

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


Teaching

Spring 2019: General Topology.


Contact

email: rachaelboyd@mpim-bonn.mpg.de

address: Max Planck Institut für Mathematik, Bonn, Germany