Objective Quantum Field Theory (QFT) has become a universal framework in physics to study systems with infinite number of degrees of freedom. It has also had in the past significant interaction with Probability starting with Constructive QFT and rigorous statistical mechanics. The goal of this proposal is to bring QFT methods to probabilistic problems and new ideas from Probability to QFT. It concentrates on two concrete topics: (1) Renormalization Group study of rough Stochastic Partial Differential Equations, both their path wise solutions and their space-time correlations and stationary states. These equations are ubiquitous in non-equilibrium physics and they are mathematically challenging. (2) The use of Multiplicative Chaos theory in the rigorous construction and study of the Liouville Conformal Field Theory. Liouville theory is one of the most studied Conformal Field Theories in physics due to its connection to scaling limits of random surfaces and string theory. It has many mathematically puzzling features and its rigorous study is now possible. Although the physical applications of these theories are far apart on the level of mathematical methods they have a common unity based on renormalization theory that I want to utilize. I think time is ripe for a new fruitful interaction between QFT and Probability. Fields of science natural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesphysical sciencesclassical mechanicsstatistical mechanicsnatural sciencesmathematicsapplied mathematicsmathematical physicsconformal field theorynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2016-ADG - ERC Advanced Grant Call for proposal ERC-2016-ADG See other projects for this call Funding Scheme ERC-ADG - Advanced Grant Coordinator HELSINGIN YLIOPISTO Net EU contribution € 2 463 412,00 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 (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all HELSINGIN YLIOPISTO Finland Net EU contribution € 2 463 412,00 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
