Richard

I am a reader 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-young@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.

I am an organiser of the Scottish Topology Seminar.

My CV is out of date.

Articles

  • Bigraded path homology and the magnitude-path spectral sequence
    Joint with Emily Roff.
    Submitted
    arXiv.
  • The Reachability Homology of a Directed Graph
    Joint with Emily Roff.
    Int. Math. Res. Not. IMRN. To appear
    arXiv.
  • The homology of the Temperley-Lieb algebras
    Joint with Rachael Boyd.
    Geom. Topol. 28 (2024), no. 3, 1437–1499.
    arXiv. Paper.
  • The homology of the Temperley-Lieb algebras
    Joint with Rachael Boyd.
    Geom. Topol. 28 (2024), no. 3, 1437–1499.
    arXiv. Paper.
  • The homology of the partition algebras
    Joint with Rachael Boyd and Peter Patzt.
    Pacific J. Math. 327 (2023), no. 1, 1–27.
    Article. arXiv.
  • Groups of convex bodies
    Geom. Dedicata 217 (2023), no. 4, Paper No. 76, 17 pp.
    arXiv. Paper.
  • Homological stability for Iwahori-Hecke algebras
    J. Topol. 15 (2022), no. 4, 2174–2215.
    arXiv. Paper.
  • Magnitude cohomology
    Math. Z. 301, 3617–3640 (2022)
    arXiv. Paper.
  • The homology of the Brauer algebras
    Joint with Rachael Boyd and Peter Patzt.
    Selecta Math. 27 (2021), no.5, Paper No. 85.
    Article. arXiv.
  • Combinatorics of injective words for Temperley-Lieb algebras
    Joint with Rachael Boyd.
    J.Combin.Theory Ser.A 181 (2021)
    Article. arXiv.
  • Persistent magnitude
    Joint with Dejan Govc.
    Journal of Pure and Applied Algebra 225 (2021) 106517.
    Article. 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