RIGHT NOW: working on deferred groups (aka groups are all the same), emergent algebra, recursive(?) statistics, hamiltonians with dissipation, thermodynamics, damage. (Names may change.)
See down the page for past/present published work and research subjects.

I have a mostly research blog/open notebook with more than 600 articles.

CLAIM: It is possible to build molecular computers, in a new way. For the experts: I believe there exists an encoding of chemlambda molecules, in such a way that the chemlambda model can be realized via real chemistry. Public resources are Chemlambda strings and the paired needs repository.

ABOUT ME: I practice Open Science. Really open.
  • I explain why Open Science is something you should think about in this interview (archived version) where I'm kindly presented as "a researcher who started doing "open science" even before the term was actually coined".
  • As an experiment, between 2015-2016 I tried to use social media for Open Science. It resulted in very high public exposure because it is both visually appealing and based on rigorous research. The chemlambda collection (direct access list of posts) contains more than 350 animations obtained from simulations using the Chemlambda repository, which can be independently validated by using the Library of chemlambda molecules. It was featured by Google and viewed more than 50 million times. The experiment was successful, I hope to replicate it at a large scale.

VALIDATION vs PEER-REVIEW: There is no rational doubt that it is technically possible to replace peer-review, which is a social form of validation, by a more rigorous version: give all to the reader, proofs, programs, data and let the reader form an opinion based on that. As an example is this experimental GitHub article which "runs in the browser" and comes with all means for validation: Molecular computers. That is why I believe that GitHub, as a (temporary) example, already answered, in principle, to the question: how will we collaborate, communicate, do research in the Net era?

I signed the San Francisco Declaration on Research Assessment (DORA), as well as The Cost of Knowledge.
If you care about which licence to use for your work, then CC BY 4.0 International is a good choice, because it forbids downstream restrictions on the dissemination of your work. Any licence which does the same is as good as this one. Truth is that licences become less important than DRM, which controls the ways the reader has access to the licensed work.

MORE: I have a Habilitation à diriger des recherches en Sciences Mathématiques (download the thesis), (diploma scan), USTL (Lille I), France (2007). See also my Scholar profile.

:: Chemlambda / Distributed GLC / Computing with space
:: Spaces with dilations / Sub-Riemannian geometry / Non-euclidean analysis
:: Bipotentials / Hamiltonian inclusions / Majorization and quasiconvexity
:: Variational methods in brittle fracture

(working version)- Open Science and Open Access, version 25.09.2017 (2017)
(DOI) (pdf with links)- Chemlambda strings, version 02.01.2018, (html version 15.04.2017)
(DOI)- The Chemlambda collection of simulations (2017)
(arxiv) - Geometric Ruzsa triangle inequality in metric spaces with dilations. (updated 2016)
(journal) (arxiv) - A symplectic Brezis-Ekeland-Nayroles principle,   with Géry de Saxcé, Mathematics and Mechanics of Solids 22, 6, (2017)
(GitHub)- The library of chemlambda molecules (2016), instructions to use here
(GitHub)- Turing machines, chemlambda style (2015)
(GitHub)- Molecular computers (2015)
(DOI) (journal)- Build a molecular computer. Journal of Brief Ideas (2015)
(DOI) (arxiv) - Zipper logic. 16 pages, 24 colour figures.
(MIT Press free download) (arxiv) - Chemlambda, universality and self-multiplication. 8 pages, 21 colour figures. with Louis H. Kauffman, presented at ALIFE 14
(arxiv) - GLC actors, artificial chemical connectomes, topological issues and knots. with Louis H. Kauffman
(DOI) (arxiv) - Chemical concrete machine.
(journal) (arxiv) - Graphic lambda calculus. Complex Systems 22, 4 (2013), 311-360
(arxiv) - Origin of emergent algebras.
(arxiv) - On graphic lambda calculus and the dual of the graphic beta move.
(arxiv) - Graphic lambda calculus and knot diagrams, see also the posts under the tag graphic lambda calculus at chorasimilarity.
(arxiv) - Local and global moves on locally planar trivalent graphs, lambda calculus and lambda-Scale
(arxiv) - Sub-riemannian geometry from intrinsic viewpoint, Course notes, based mainly on A characterization..., for a course at CIMPA research school on sub-riemannian geometry (2012)
(arxiv) - Lambda-Scale, a lambda calculus for spaces with dilations (update 23.05.2012), see also the posts at chorasimilarity
(arxiv) - Emergent algebras
(journal) (arxiv) - A variational formulation for constitutive laws described by bipotentials,   with Géry de Saxcé and Claude Vallée, Mathematics and Mechanics of Solids 18(2013), no. 1, 78-90
(arxiv) - Maps of metric spaces, slightly edited appendix of Computing with space..., see also these slides of the talk "Non-euclidean analysis of dilation structures"
(arxiv) - Normed groupoids with dilations, improved version of Deformations of normed groupoids
(arxiv)- Computing with space: a tangle formalism for chora and difference
(book chapter)(arxiv)- Braided spaces with dilations and sub-riemannian symmetric spaces. in: Geometry. Exploratory Workshop on Differential Geometry and its Applications, eds. D. Andrica, S. Moroianu, Cluj-Napoca 2011, 21-35
(journal)(pdf) (arxiv) - A characterization of sub-riemannian spaces as length dilation structures constructed via coherent projections, Commun. Math. Anal. 11 (2011), No. 2, pp. 70-111
(journal) (arxiv) - Blurred constitutive laws and bipotential convex covers,   with Géry de Saxcé and Claude Vallée, Mathematics and Mechanics of Solids 16(2), (2011), 161-171
(journal)(pdf) - A priori inequalities between energy release rate and energy concentration for 3D quasistatic brittle fracture propagation, Mathematics and Mechanics of Solids, vol. 16 (2011), no.3, 265-282, DOI 10.1177/1081286510375347
(journal) (pdf) (arxiv) - Infinitesimal affine geometry of metric spaces endowed with a dilatation structure, Houston Journal of Mathematics, 36, 1 (2010), 91-136
(journal) (arxiv) - Blurred maximal cyclically monotone sets and bipotentials, with Géry de Saxcé and Claude Vallée, Analysis and Applications 8 (2010), no. 4, 1-14
(journal) (arxiv) - Bipotentials for non monotone multivalued operators: fundamental results and applications, with Géry de Saxcé and Claude Vallée, Acta Applicandae Mathematicae, 110, 2(2010), 955-972
(journal) (arxiv) - Non maximal cyclically monotone graphs and construction of a bipotential for the Coulomb's dry friction law, with Géry de Saxcé and Claude Vallée, J. of Convex Analysis 17, No 1. (2010), 81-94
(arxiv) (FQXi essay) - More than discrete or continuous: a bird's view
(arxiv) - Boring mathematics, artistes pompiers and impressionists
(arxiv) - What is a space? Computations in emergent algebras and the front end visual system
(arxiv) - Introduction to metric spaces with dilations
(journal) (arxiv) - Hamiltonian inclusions with convex dissipation with a view towards applications, Mathematics and its Applications 1, 2 (2009), 228-251