Objective The goal of my mathematical research is to force a breakthrough in solving and understanding a number of long-standing open problems that are rooted in physics and chemistry. My objects of study are systems consisting of a large number of random components that interact locally but exhibit a global dependence. Typically, the components of these systems are subject to a simple microscopic dynamics. The challenge lies in understanding the complex macroscopic phenomena that may arise from this dynamics. Core to my proposal are macroscopic phenomena that are very hard to grasp with heuristic or numerical methods: pinning, localisation, collapse, porosity, nature vs. nurture, metastability, condensation, ageing, catalysis, intermittency and trapping. My main line of attack is to combine large deviation theory, which is a well-established technically demanding yet flexible instrument, with a number of new variational techniques that I have recently developed with my international collaborators, which are based on space-time coarse-graining. My goal is to apply this powerful combination to a number of complex systems that are at the very heart of the research area, in order to arrive at a complete mathematical description. The idea is to use the coarse-graining techniques to compute the probability of the possible trajectories of the microscopic dynamics, and to identify the most likely trajectory by maximising this probability in terms of a variational formula. The solution of this variational formual is what describes the macroscopic behaviour of the system, including the emergence of phase transitions. My proposal focuses on five highly intriguing classes of random interacting systems that are among the most challenging to date: (1) polymer chains; (2) porous domains; (3) flipping magnetic spins; (4) lattice gases; (5) evolving random media. The unique reward of the variational approach is that it leads to a full insight into why these systems behave the way they do. Fields of science natural scienceschemical sciencespolymer sciencesnatural scienceschemical sciencescatalysisnatural sciencescomputer and information sciencesartificial intelligenceheuristic programmingnatural sciencesmathematicsapplied mathematicsnumerical analysis Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2010-AdG_20100224 See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Host institution UNIVERSITEIT LEIDEN EU contribution € 1 930 000,00 Address RAPENBURG 70 2311 EZ Leiden Netherlands See on map Region West-Nederland Zuid-Holland Agglomeratie Leiden en Bollenstreek Activity type Higher or Secondary Education Establishments Principal investigator Wilhelmus Theodorus Franciscus Den Hollander (Prof.) Administrative Contact Tonnis Brouwer Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all UNIVERSITEIT LEIDEN Netherlands EU contribution € 1 930 000,00 Address RAPENBURG 70 2311 EZ Leiden See on map Region West-Nederland Zuid-Holland Agglomeratie Leiden en Bollenstreek Activity type Higher or Secondary Education Establishments Principal investigator Wilhelmus Theodorus Franciscus Den Hollander (Prof.) Administrative Contact Tonnis Brouwer Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
