Since July 2011 I have been a lecturer in the Institute for Mathematics at the University of Aberdeen. Before that I held postdoctoral positions at the University of Copenhagen and the University of Sheffield, and I studied for my PhD at Edinburgh University.

My research is in the area called Algebraic Topology.

I currently teach the courses MA1005 Calculus I and MX4540 Knots. You are welcome to take a look at my Knots Notes and Knots Videos. (Current students, please use MyAberdeen to make sure you get the newest version!)

Rachael Boyd is my PhD student.

I am an organiser of the Scottish Topology Seminar.

My CV is sometimes up to date.

Research Projects

  • I recently wrote a paper on homological stability for Coxeter groups. I show that for certain sequences of Coxeter groups \[W_1\hookrightarrow W_2\hookrightarrow W_3\hookrightarrow\cdots\] the resulting sequence of homology groups \[H_\ast(W_1)\rightarrow H_\ast(W_2)\rightarrow H_\ast(W_3)\rightarrow\cdots\] eventually consists of isomorphisms in each degree. The sequences in question include the families of type \(A_n\), \(B_n\) and \(D_n\), and in particular we recover Nakaoka's homological stability result for the symmetric group. I plan to continue this line of research, perhaps by considering \(H_\ast(W_\infty)\) or \(H^\ast(W_n;\mathbb{Z}W_n)\). Slides from a talk on this work.

  • Anssi Lahtinen and I wrote a paper on string topology of classifying spaces. We show that if \(G\) is a compact Lie group then the homology \(H_\ast(LBG)\) admits a rich algebraic structure, similar to a homological conformal field theory, but with 1-manifolds, surfaces and diffeomorphisms replaced with homotopy-theoretical analogues that we call "h-graphs".

    Lahtinen has a recent paper showing that in this setting there is an abundant supply of non-trivial higher operations. As a consequence he obtains interesting classes in the homology of groups like \(Aut(F_n)\).

    Notes from a talk. Notes from lectures at Loop spaces in geometry and topology. Slides from a talk by Lahtinen.

What do I do?

When people ask me what I do for a living, I say that I am a maths lecturer. For most people, including my family, friends, students, and probably some colleagues, it's hard to imagine what that means, and in fact I often find it hard to say. So I've started writing a page that tries to give some answers. Read it here.


  • Email:
    r.hepworth AT
  • Office:
    Fraser Noble Building, Room 159
  • Telephone:
    01224 272751
  • Postal:
    Richard Hepworth
    Institute of Mathematics
    University of Aberdeen
    Aberdeen AB24 3UE
    United Kingdom


  • Categorifying the magnitude of a graph
    Joint with Simon Willerton
  • Homological stability for families of Coxeter groups.
  • On string topology of classifying spaces.
    Joint with Anssi Lahtinen
    Adv. Math. 281 (2015) 394-507.
    Article. arXiv.
  • Configuration spaces and \(\Theta_n\).
    Joint with David Ayala
    Proc. Amer. Math. Soc. 142 (2014), no.7, 2243-2254.
    Article. arXiv.
  • Groups, cacti and framed little discs.
    Trans. Amer. Math. Soc. 365(2013), 2597 - 2636
    Article. arXiv.
  • String Topology for complex projective spaces.
  • String Topology for Lie Groups.
    J. Topology (2010) 3(2): 424-442.
    Abstract. Article. arXiv.
  • Vector fields and flows on differentiable stacks.
    Theory Appl. Categ, Vol. 22, No. 21, 2009, pp. 542-587.
    Abstract. Article. arXiv.
  • Morse Inequalities for Orbifold Cohomology.
    Algebr. Geom. Topol. 9 (2009) 1105-1175.
    Article. arXiv.
  • The age grading and the Chen-Ruan cup product.
    Bull. London Math. Soc. (2010) 42(5): 868-878
    Abstract. Article. arXiv.
  • The topology of certain 3-Sasakian 7-Manifolds.
    Math. Ann. 339 (2007), no. 4, 733–755.
  • Generalized Kreck-Stolz invariants and the topology of certain 3-Sasakian 7-manifolds.
    Edinburgh University PhD Thesis, 2005.