Noncommutative geometry and physics
This is a compilation of some well known propositions of Alain Connes concerning the use of noncommutative geometry in mathematical physics.
math-ph↗
arXiv subjects
Jean Petitot
Publications and source records attributed to Jean Petitot.
Singularity theory and heat equation
The paper (in French) exemplifies graphically a solution of the heat equation which is a 1-dimensional unfolding of an elliptic umbilic catastrophe. The example is due to James Damon and adapts Thom-Mather's singularity theory to multiscale models of scale-space analysis in image processing.
math.DG↗
A transcendental view on the continuum: Woodin's conditional platonism
One of the main difficulty concerning the nature of the continuum is to do justice, inside the set theoretical Cantorian framework, to the classical conception (from Aristotle to Thom, via Kant, Peirce, Brentano, Husserl and Weyl) according to which the continuum is a non-compositional, cohesive, primitive, and intuitive datum. This paper investigates such possibilities, from Gödel to Woodin, of modelling inside a ZFC-universe the transcendence of the intuitive continuum w.r.t. its symbolic determination. Keywords: constructive universe, continuum, Gödel, forcing, Kant, large cardinals, $Ω$-logic, projective hierarchy, $V = L$, Woodin, $0^{\#}$.
math.LO↗
Le problème intensionnel de la quantification chez Hilbert (The intensional problem of quantification in Hilbert)
The paper (in French) presents a survey of Hilbert's Epsilon operator focusing on the intensional aspects of its semantics. It comments on some epistemological problems, from Albert Lautman in the 1930s to John Bell, Grigori Mints, Barry Hartley Slater, Richard Zach or Edward Zalta in the 1990s.
math.LO↗
Complexity and self-organization in Turing
We comment on Alan Turing's celebrated paper "The Chemical Basis of Morphogenesis" published in 1952 in the "Philosophical Transactions of the Royal Society of London". It is a typical example of a pioneering and inspired work in the domain of mathematical modelling.
q-bio.OT↗