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 1manifolds, surfaces and diffeomorphisms replaced with homotopytheoretical analogues that we call "hgraphs".
Lahtinen has a recent paper showing that in this setting there is an abundant supply of nontrivial 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.Contact
 Email:
r.hepworth AT abdn.ac.uk  Office:
Fraser Noble Building, Room 159  Telephone:
01224 272751  Postal:
Richard Hepworth
Institute of Mathematics
University of Aberdeen
Aberdeen AB24 3UE
United Kingdom
Articles

Categorifying the magnitude of a graph
Joint with Simon Willerton
arXiv. 
Homological stability for families of Coxeter groups.
Submitted.
arXiv. 
On string topology of classifying spaces.
Joint with Anssi Lahtinen
Adv. Math. 281 (2015) 394507.
Article. arXiv. 
Configuration spaces and \(\Theta_n\).
Joint with David Ayala
Proc. Amer. Math. Soc. 142 (2014), no.7, 22432254.
Article. arXiv. 
Groups, cacti and framed little discs.
Trans. Amer. Math. Soc. 365(2013), 2597  2636
Article. arXiv. 
String Topology for complex projective spaces.
arXiv. 
String Topology for Lie Groups.
J. Topology (2010) 3(2): 424442.
Abstract. Article. arXiv. 
Vector fields and flows on differentiable stacks.
Theory Appl. Categ, Vol. 22, No. 21, 2009, pp. 542587.
Abstract. Article. arXiv. 
Morse Inequalities for Orbifold Cohomology.
Algebr. Geom. Topol. 9 (2009) 11051175.
Article. arXiv.

The age grading and the ChenRuan cup product.
Bull. London Math. Soc. (2010) 42(5): 868878
Abstract. Article. arXiv.

The topology of certain 3Sasakian 7Manifolds.
Math. Ann. 339 (2007), no. 4, 733–755.
arxiv. 
Generalized KreckStolz invariants
and the topology of certain 3Sasakian 7manifolds.
Edinburgh University PhD Thesis, 2005.
pdf.