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Faculty of Mathematics




  • 2017-          : Nevile Research Fellow in Applied Mathematics, Magdalene College, Cambridge
  • 2016-2017 : EPSRC Doctoral Prize Fellow, DAMTP, University of Cambridge
  • 2013-2016 : PhD Student, DAMTP, University of Cambridge
  • 2009-2013 : Mathematical Tripos (BA & MMath), Gonville & Caius College, Cambridge


Pierre is a member of the Biological Physics research group in the Department of Applied Mathematics and Theoretical Physics. His research is on the mathematics of morphogensis: how does shape arise in physical systems, living or otherwise?

Inversion in Volvox

The inversion process in the green alga Volvox, spherical sheets of cells that turn themselves inside out through a small hole at the top, is a model for morphogenesis. A series of papers explores the mechanical underpinnings of this process.

  1. S. Höhn, A. R. Honerkamp-Smith, P. A. Haas, P. Khuc Trong, and R. E. Goldstein, "Dynamics of a Volvox Embryo Turning Itself Inside Out", Physical Review Letters 114, 178101 (2015), selected for a Viewpoint in Physics: A. Boudaoud, "How to Turn an Embryo Inside Out", Physics 8, 39 (2015).
  2. P. A. Haas and R. E. Goldstein, "Elasticity and Glocality: Initiation of Embryonic Inversion in Volvox", J. R. Soc. Interface 12, 20150671 (2015).
  3. P. A. Haas, S. S. M. H. Höhn, A. R. Honerkamp-Smith, J. B. Kirkegaard, and R. E. Goldstein, "The noisy basis of morphogenesis: Mechanisms and Mechanics of Cell Sheet Folding Inferred from Developmental Variability", PLOS Biology 16, e2005536 (2018).
  4. P. A. Haas and R. E. Goldstein, "Embryonic Inversion in Volvox carteri: The Flipping and Peeling of Elastic Lips", Physical Review E 98, 052415 (2018), highlighted as an Editors' Suggestion.

Other Research

The continuum constitutive laws describing active material such as epithelial tissues are poorly understood. Taking an explicit continuum limit of a simple discrete model of an epithelium, we have shown how cell-level properties lead to nonlinear and nonlocal behaviour at the continuum level.

  • P. A. Haas and R. E. Goldstein, "Nonlinear and Nonlocal Elasticity in Coarse-Grained Differential-Tension Models of Epithelia", Physical Review E 99 (2019, in press), arXiv:1810.09259.

Shape generating chemical systems are a very literal instantiation of Turing's quest for the chemical basis of morphogenesis. In collaboration with experimental groups, we have developed a theory describing a recently discovered exemplar of such a system: oil emulsion droplets that flatten into a variety of polygonal shapes upon slow cooling.

Another research interest centres around probabilistic models for the prediction of RNA secondary structures, in particular extending models based on stochastic context-free grammars to include kinetic transcription effects.


  • 2017 : APS Division of Biological Physics Award for Outstanding Doctoral Thesis Research in Biological Physics: Citation
  • 2013 : Mayhew Prize



Embryonic Inversion in
PA Haas, RE Goldstein
– Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
Nonlinear and nonlocal elasticity in coarse-grained differential-tension models of epithelia
PA Haas, RE Goldstein
– Phys Rev E
The noisy basis of morphogenesis: Mechanisms and mechanics of cell sheet folding inferred from developmental variability.
PA Haas, SSMH Höhn, AR Honerkamp-Smith, JB Kirkegaard, RE Goldstein
– PLoS Biol
Theory of Shape-Shifting Droplets.
PA Haas, RE Goldstein, SK Smoukov, D Cholakova, N Denkov
– Physical review letters
Elasticity and glocality: Initiation of embryonic inversion in Volvox
PA Haas, RE Goldstein
– Journal of the Royal Society, Interface
Dynamics of aVolvoxEmbryo Turning Itself Inside Out
S Höhn, AR Honerkamp-Smith, PA Haas, PK Trong, RE Goldstein
– Phys Rev Lett
Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information.
JWJ Anderson, PA Haas, L-A Mathieson, V Volynkin, R Lyngsø, P Tataru, J Hein
– Bioinformatics (Oxford, England)

Research Group

Biological Physics and Mechanics




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