Richard

I am a senior lecturer in the Institute of Mathematics at the University of Aberdeen, where I have worked since 2011. 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.

Contact:
Email: r.hepworth@abdn.ac.uk
Office: Fraser Noble 159

Research:
My research is in Algebraic Topology. Currently this has two strands: Homological stability, which studies sequences of groups (such as the symmetric groups or general linear groups) and how their homology changes as you proceed along the sequence; recently I (and my collaborators) have successfully extended this technique to study algebras in place of groups. And Magnitude homology, which is a categorification of Tom Leinster's notion of magnitude introduced by Simon Willerton and myself; this new notion has led to a lot of new work, including connections to metric geometry and curvature. In the past I have worked on string topology, operads, and 7-manifolds.

Teaching:
I currently teach the courses EG2012 Engineering Mathematics 2 and MX4540 Knots. I am also the Retention officer for mathematics, meaning that I try to offer advice and help to students who may be having difficulties with their studies.

Scottish Mathematical Challenge:
I am the organiser for the Scottish Mathematical Challenge in the North.
Main website: link
Website for teachers: link
Teachers and pupils are welcome to get in touch with me with any questions or issues.

I am an organiser of the Scottish Topology Seminar.

My CV.

Articles

  • Homological stability for Temperley-Lieb algebras
    Joint with Rachael Boyd.
    Submitted.
    arXiv. pdf.
  • Homological stability for Iwahori-Hecke algebras
    Submitted.
    arXiv. pdf.
  • Combinatorics of injective words for Temperley-Lieb algebras
    Joint with Rachael Boyd.
    Submitted
    arXiv. pdf.
  • Magnitude cohomology
    Submitted.
    arXiv.
  • Persistent magnitude
    Joint with Dejan Govc.
    To appear in Journal of Pure and Applied Algebra.
    arXiv.
  • On the edge of the stable range
    Mathematische Annalen (2020) 377:123-181.
    Article. arXiv. pdf.
  • Categorifying the magnitude of a graph
    Joint with Simon Willerton
    Homology Homotopy Appl. 19(2), 2017, pp.31–60.
    Article. arXiv.
  • Homological stability for families of Coxeter groups.
    Algebr. Geom. Topol. 16 (2016) 2779–2811.
    Article. arXiv.
  • 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.
    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.

A Course in Knot Theory