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.

### 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
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.
arXiv.
• 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.
arxiv.
• Generalized Kreck-Stolz invariants and the topology of certain 3-Sasakian 7-manifolds.
Edinburgh University PhD Thesis, 2005.
pdf.