Objective "Recent years have seen an explosion of applications of geometric and pathwise ideas in probability theory, with motivations from fields as diverse as quantitative finance, statistics, filtering, control theory and statistical physics. Much can be traced back to Bismut, Malliavin (1970s) on the one-hand and then Doss, Sussman (1970s), Foellmer (1980s) on the other hand, with substantial new input from Lyons (from '94 on), followed by a number of workers, including Gubinelli (from '04 on) and the writer of these lines (also from '04 on). Most recently, the theory of such ``rough paths"" has been extended to ``rough fields"", notably in the astounding works of M. Hairer (from '13 on). The purpose of this project is to study a number of important problems in this field, going beyond the rough path setting, and with emphasis on geometric ideas. (i) The transfer of concepts from rough path theory to the new world of Hairer's regularity structures.(ii) Applications of geometric and pathwise ideas in quantitative finance.(iii) Obtain a pathwise understanding of the geometry of Loewner evolution and more generally explore the use of rough path-inspired ideas in the world of Schramm-Loewner evolution.(iv) Investigate the role of geometry in the pathwise analysis of non-linear evolution equations." Fields of science social sciencespolitical sciencespolitical transitionsrevolutionsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicsapplied mathematicsstatistics and probabilitynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Keywords Pathwise stochastic analysis Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-CoG-2015 - ERC Consolidator Grant Call for proposal ERC-2015-CoG See other projects for this call Funding Scheme ERC-COG - Consolidator Grant Coordinator TECHNISCHE UNIVERSITAT BERLIN Net EU contribution € 1 180 000,00 Address Strasse des 17 juni 135 10623 Berlin Germany See on map Region Berlin Berlin Berlin Activity type Higher or Secondary Education Establishments 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 Other funding € 0,00 Beneficiaries (2) Sort alphabetically Sort by Net EU contribution Expand all Collapse all TECHNISCHE UNIVERSITAT BERLIN Germany Net EU contribution € 1 180 000,00 Address Strasse des 17 juni 135 10623 Berlin See on map Region Berlin Berlin Berlin Activity type Higher or Secondary Education Establishments 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 Other funding € 0,00 FORSCHUNGSVERBUND BERLIN EV Germany Net EU contribution € 285 000,00 Address Rudower chaussee 17 12489 Berlin See on map Region Berlin Berlin Berlin 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 Other funding € 0,00
