Objective This proposal focuses on the mathematics of three cross-disciplinary, very active and deeply interlaced research themes: interacting particle systems with kinetic constraints, bootstrap percolation cellular automata and mixed order phase transitions. These topics belong to the fertile area of mathematics at the intersection of probability and mathematical statistical mechanics. They are also extremely important in physics. Indeed they are intimately connected to the fundamental problem of understanding the liquid-glass transition, one of the longstanding open questions in condensed matter physics.The funding of this project will allow the PI to lead a highly qualified team with complementary expertise. Such a diversity will allow a novel, interdisciplinary and potentially groundbreaking approach. Even if research on each one of the above topics has been lately quite lively, very few exchanges and little cross-fertilization occurred among them. One of our main goals is to overcome the barriers among the three different research communities and to explore the interfaces of these yet unconnected fields. We will open two novel and challenging chapters in the mathematics of interacting particle systems and cellular automata: interacting particle glassy systems and bootstrap percolation models with mixed order critical and discontinuous transitions. In order to achieve our groundbreaking goals we will have to go well beyond the present mathematical knowledge. We believe that the novel concepts and the unconventional approaches that we will develop will have a deep impact also in other areas including combinatorics, theory of randomized algorithms and complex systems. The scientific background and expertise of the PI, with original and groundbreaking contributions in each of the above topics and with a broad and clearcut vision of the mathematics of the proposed research as well as of the fundamental physical questions,make the PI the ideal leader of this project. Fields of science natural scienceschemical sciencesinorganic chemistryalkali metalsnatural scienceschemical sciencesinorganic chemistryinorganic compoundsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesphysical sciencesclassical mechanicsstatistical mechanicsnatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Keywords interacting particle systems bootstrap percolation liquid-glass transition glassy dynamics cellular automata mathematical statistical mechanics Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-StG-2015 - ERC Starting Grant Call for proposal ERC-2015-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Host institution CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Net EU contribution € 883 250,00 Address RUE MICHEL ANGE 3 75794 Paris France See on map Region Ile-de-France Ile-de-France Paris Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 883 250,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS France Net EU contribution € 883 250,00 Address RUE MICHEL ANGE 3 75794 Paris See on map Region Ile-de-France Ile-de-France Paris Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 883 250,00
