Project description DEENESFRITPL Mathematical models to explain natural phenomena: tomography, turbulence and random tilings Scaling invariance occurs in different forms in many natural phenomena. A well known example of a rough scale invariance is the fractal nature of a shoreline. From a mathematical point, explaining and making use of the scale invariance leads to the method of conformal (shape preserving) and quasiconformal mappings (that preserve shapes only roughly). Fourier analysis, where one decomposes a signal into its constituent frequencies, provides a related approach to analyse complicated natural phenomena. QUAMAP is devoted to applying aspects of modern mathematical analysis, from quasiconformal mappings to Fourier analysis, to several problems arising in mathematical physics. Using these tools, along with nonlinear analogues, the project hopes to shed light on diverse challenging problems including the geometry of energy minimisers, scaling limits in random geometry, an imaging technique based on electrical surface measurements, as well as the behaviour of fluids in turbulent regimes. Show the project objective Hide the project objective Objective The use of delicate quasiconformal methods, in conjunction with convex integration and/or nonlinear Fourier analysis, will be the common theme of the proposal. A number of important outstanding problems are susceptible to attack via these methods. First and foremost, Morrey's fundamental question in two dimensional vectorial calculus of variations will be considered as well as the related conjecture of Iwaniec regarding the sharp $L^p$ bounds for the Beurling transform. Understanding the geometry of conformally invariant random structures will be one of the central goals of the proposal. Uhlmann's conjecture regarding the optimal regularity for uniqueness in Calder\'on's inverse conductivity problem will also be considered, as well as the applications to imaging. Further goals are to be found in fluid mechanics and scattering, as well as the fundamental properties of quasiconformal mappings, interesting in their own right, such as the outstanding deformation problem for chord-arc curves. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisfourier analysisnatural sciencesmathematicspure mathematicsgeometry Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2018-ADG - ERC Advanced Grant Call for proposal ERC-2018-ADG See other projects for this call Funding Scheme ERC-ADG - Advanced Grant Coordinator HELSINGIN YLIOPISTO Net EU contribution € 1 107 138,75 Address Yliopistonkatu 3 00014 Helsingin yliopisto Finland See on map Region Manner-Suomi Helsinki-Uusimaa Helsinki-Uusimaa 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 (4) Sort alphabetically Sort by Net EU contribution Expand all Collapse all HELSINGIN YLIOPISTO Finland Net EU contribution € 1 107 138,75 Address Yliopistonkatu 3 00014 Helsingin yliopisto See on map Region Manner-Suomi Helsinki-Uusimaa Helsinki-Uusimaa 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 UNIVERSIDAD AUTONOMA DE MADRID Spain Net EU contribution € 405 750,00 Address Calle einstein 3 ciudad univ cantoblanco rectorado 28049 Madrid See on map Region Comunidad de Madrid Comunidad de Madrid Madrid 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 AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS Spain Net EU contribution € 366 100,00 Address Calle serrano 117 28006 Madrid See on map Region Comunidad de Madrid Comunidad de Madrid Madrid 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 AALTO KORKEAKOULUSAATIO SR Participation ended Finland Net EU contribution € 401 361,25 Address Otakaari 1 02150 Espoo See on map Region Manner-Suomi Helsinki-Uusimaa Helsinki-Uusimaa 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
