The spectacular success of probability theory within the hard sciences is well known since its pivotal role in the statistical mechanics approach to thermodynamics. It is interesting to notice, nevertheless, that when probability was first included into a higher mathematics curriculum, it was with the purpose to approach socio-economic problems:
“Enfin, on donnera les principes de la théorie des probabilités. Dans un temps où tous les citoyens sont appelés à décider du sort de leurs semblables, il leur importe de connaître une science qui fait apprécier, aussi exactement qu’il est possible, la probabilité des témoignages, et celle qui résulte des circonstances dont les faits sont accompagnés : il importe surtout de leur apprendre à se défier des aperçus même les plus vraisemblables ; et rien n’est plus propre à cet objet que la théorie des probabilités, dont souvent les résultats rigoureux sont contraires à ces aperçus. D’ailleurs, les nombreuses applications de cette théorie, aux naissances, aux mortalités, aux élections et aux assurances, applications qu’il est avantageux de perfectionner et d’étendre à d’autres objets, la rendent une des parties les plus utiles des connaissances humaines”

from Lagrange and Laplace opening lecture at Ecole Normale, January 20th 1795

In the past however, the application of probabilistic methods to problems of this type, has never gone beyond minor achievements, apart perhaps from a few exceptions. Recently though, the availability of large databases and the advent of computer facilities has created a fertile ground for probabilistic methods to grow, especially when they originate from statistical mechanics. At the same time the progresses made in the last decades in the studies of non-homogenous disordered systems have produced new promising approaches and technical tools for applied research topics.
The trimester aims at bringing together scientists working on the following three topical areas, with strong common cultural roots and wide research interest intersections:
  1. probabilistic methods on random spatial processes, for instance on growth models, percolation, coalescence, non-equilibrium phase transitions.
  2. statistical mechanics of interacting particle systems, especially disordered models like spin glasses, diluted systems, directed and pinned polymers.
  3. “complex systems” approached with mathematical and physical methods, in particular agent based models applied to socio-economic problems, inverse problems, multi-fractal models.
The program, anchored around those three main topics and subtopics, will be built on a school, three one-week workshops, various mini-symposia, research group meetings and three open lectures for a wide public audience.