Career
 20172020 : Nevile Research Fellow in Applied Mathematics, Magdalene College, Cambridge
 20162017 : EPSRC Doctoral Prize Fellow, DAMTP, University of Cambridge
 20132016 : PhD Student, DAMTP, University of Cambridge
 20092013 : 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 This page is therefore no longer updated.
Research
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.
 S. Höhn, A. R. HonerkampSmith, 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).
 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).
 P. A. Haas, S. S. M. H. Höhn, A. R. HonerkampSmith, 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).
 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.
 P. A. Haas, R. E. Goldstein, S. K. Smoukov, D. Cholakova, and N. Denkov, "Theory of ShapeShifting Droplets", Physical Review Letters 118, 088001 (2017).
 P. A. Haas, D. Cholakova, N. Denkov, R. E. Goldstein, and S. K. Smoukov, "ShapeShifting 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 celllevel properties lead to nonlinear and nonlocal behaviour at the continuum level.
 P. A. Haas and R. E. Goldstein, "Nonlinear and Nonlocal Elasticity in CoarseGrained DifferentialTension Models of Epithelia", Physical Review E 99, 022411 (2019).
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 LotkaVolterra models of competing species. In particular, we reveal the surprising stabilising effect of a rare phenotype.
 P. A. Haas, N. M. Oliveira, and R. E. Goldstein, "Subpopulations and Stability in Microbial Communities", Physical Review Research (Rapid Communications) 2, 022036(R) (2020).
Another research interest centres around probabilistic models for the prediction of RNA secondary structures, in particular extending models based on stochastic contextfree grammars to include kinetic transcription effects.

J. W. J. Anderson, P. A. Haas, L.A. Mathieson, V. Volynkin, R. Lyngsø, P. Tataru, and J. Hein, "Oxfold: kinetic folding of RNA using stochastic contextfree grammars and evolutionary information", Bioinformatics 29, 704 (2013).
Commentary
 P. A. Haas, "Morphogenesis: Mathematical Models with Frills", eLife 8, e48520 (2019), Insight article highlighting S. A. Montandon, A. Fofonjka, and M. C. Milinkovitch, "Elastic instability during branchial ectoderm development causes folding of the Chlamydosaurus erectile frill", eLife 8, e44455 (2019).
Awards
 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.)
Publications
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