:: Emergent algebra / Computing with space / Graphical calculi

:: Spaces with dilations / Sub-Riemannian geometry / Non-euclidean analysis

:: Bipotentials / Hamiltonian inclusions / Majorization and quasiconvexity

:: Variational methods in brittle fracture

(arxiv) - Origin of emergent algebras.

(arxiv) - Geometric Ruzsa triangle inequality in metric spaces with dilations.

(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 (2012)

(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