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Quantum Fields and Probability

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.

Call for proposal

ERC-2016-ADG
See other projects for this call

Host institution

HELSINGIN YLIOPISTO
Address
Yliopistonkatu 3
00014 Helsingin Yliopisto
Finland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 2 463 412

Beneficiaries (1)

HELSINGIN YLIOPISTO
Finland
EU contribution
€ 2 463 412
Address
Yliopistonkatu 3
00014 Helsingin Yliopisto
Activity type
Higher or Secondary Education Establishments