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Faculty of Mathematics



  • 2017-2020 : 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

In June 2020, I moved to the University of Oxford (the "Other Place") to take up a Hooke Research Fellowship at the Mathematical Institute. This page is therefore no longer updated.


I am a research fellow in the Biological Physics research group in the Department of Applied Mathematics and Theoretical Physics. I am an applied mathematician, and my research is at the interface of biophysics, soft matter physics, and mathematical biology. A brief discussion of my research interests follows below.

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", Journal of the Royal Society 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

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.

  1. P. A. Haas, R. E. Goldstein, S. K. Smoukov, D. Cholakova, and N. Denkov, "Theory of Shape-Shifting Droplets", Physical Review Letters 118, 088001 (2017).
  2. P. A. Haas, D. Cholakova, N. Denkov, R. E. Goldstein, and S. K. Smoukov, "Shape-Shifting Polyhedral Droplets", Physical Review Research 1, 023017 (2019).

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.

The classical question of theoretical ecology is: is coexistence in a population model stable? We have explored the effect of subpopulation structure (such as phenotypic variation) on the stability of coexistence in Lotka-Volterra models of competing species. In particular, we reveal the surprising stabilising effect of a rare phenotype.

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

(An automatically generated list of publications follows below.)


Using in vivo Optical Sectioning to Investigate Mechanical Aspects of Volvox Development
AR Honerkamp-Smith, S Hoehn, H Wioland, PA Haas, PK Trong, RE Goldstein
– Biophysical Journal
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
Subpopulations and Stability in Microbial Communities
PA Haas, NM Oliveira, RE Goldstein
Morphoelasticity of Large Bending Deformations of Cell Sheets during Development
PA Haas, RE Goldstein
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Research Group

Biological Physics and Mechanics




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