CLASS

The project focuses on the relation between integrable many-body systems and three important fields of mathematics: partial differential equations, Painlevé equations, and probability theory. The goal is to build new connections in this context by considering recent results as follows. The first objective consists in explaining how a class of integrable many-body systems that appeared over the last 5 years can be used to parametrise specific solutions to hierarchies of partial differential equations. An algebraic and a geometric interpretation of these parametrisations will be sought. The second objective deals with the extension of the Hamiltonian formulation of many-particle Painlevé equations, called the Calogero-Painlevé correspondence, to new cases. This investigation will make a central use of the current activity on discrete Painlevé equations and the quantum analogues of Painlevé equations. The third objective related to probability theory is two-fold. On the one hand, quantum versions of integrable many-body systems will be derived by adding noise to specific diffusion processes that are constructed using their classical versions. On the other hand, important properties of probability distributions appearing in random matrix theory or the study of beta ensembles will be obtained. The point of view will be to interpret these distributions in terms of suitable many-body systems whose integrability will play a key role for the computation of the desired properties.

It is widely recognised that non-medical determinants of health play a major role in health. Many of these determinants fall within the scope of Social Sciences and Humanities (SSH). World Health Organisation estimates that Social determinants of health (housing and working conditions, social inequalities, education, etc.) account for between 30-55% of health outcomes. Today, there are urgent needs of profiles capable of understanding the issues in their entirety rather than through a strictly health or social point of view. BREATH program will fill that gap by training excellent researchers. BREATH aims to be the next interdisciplinary Doctoral Program in Health and SSH, offering 20 doctoral positions for 3 years each at one of the 3 Pays-de-la-Loire Universities in France, led by distinguished supervisors. Through an open and merit-based recruitment procedure, it will provide excellent opportunities for international, intersectoral and interdisciplinary research and training under attractive working conditions. BREATH is coordinated by the University of Angers, with the Universities of Nantes and Le Mans as implementing partners. The 3 public universities have long-standing habits of strong collaboration in doctoral studies, already managed jointly by the Doctoral College, with 83 research groups including 49 in Health and SSH. BREATH will also rely on a 27 associated partners network that will strongly enhance the opportunities of the Doctoral Candidates (DCs). DCs will come closer to the private sector by collaborating with medical and healthcare organisations during secondments or special events. Beyond training through their own research, they will benefit from training courses in research techniques, complementary workshops for transferable skills, scientific meetings and conferences and the access to international scientific networks, with the final aim to promote knowledge exchange and mobility among academic and non academic partners.