Mark Penney

Postdoctoral Fellow,
Max Planck Institute for Mathematics

e-mail: mpenney [at]

About Me

I currently hold a postdoctoral fellowship at the Max Planck Institute, having just received my DPhil from Oxford in September 2017 under the supervision of Chris Douglas. For more detailed information about my academic past please see my CV.

I am working in mathematical physics, specifically the portion straddling and drawing connections between theoretical physics, representation theory, higher categories and homotopy theory. The unifying structure is that of a topological field theory. My own research has so far focused on Hopf categories and their use in 4-dimensional topological field theory. I also have an ongoing interest in quantum information theory, particularly the use of path integral techniques to understand notions of classicality.

Research Papers


  1. Computing quopit Clifford circuit amplitudes via sum-over-paths. With Dax E Koh and Robert W Spekkens. Quantum Information & Computation , Vol. 17, No. 13&14 (2017) 1081–1095

    Available at: arXiv, journal, pdf

  2. Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths? With Dax E Koh and Robert W Spekkens. New Journal of Physics (2017) 19, 073006

    Available at: arXiv, journal, pdf

  3. Quantum measurements of scattered particles. With Marco Merkli Mathematics, (2015) Vol. 3(1), 92–118

    Available at: arXiv, journal, pdf


  1. The universal Hall bialgebra of a double 2-Segal space. Submitted

    Available at: arXiv, pdf

  2. Simplicial spaces, lax algebras and the 2-Segal conditions. Submitted

    Available at: arXiv, pdf

Other Writings

  1. Categorical bialgebras arising from 2-Segal spaces. DPhil Thesis

    Available at: pdf


During the winter semester 2019 I will be teaching a selected topics course on the little n-discs operad. Class details can be found here.