In recent years, the probabilistic point of view has become increasingly important in a wide range of important problems in pure and applied quantitative sciences. A notable example of this is random geometry, which studies random geometrical objects that arise in classical and quantum statistical physics. Our teams have been at the forefront of mathematical developments in random geometry, which have made Finland a major international center in this new vibrant field. In FiRST, we will continue our groundbreaking work in analytic number theory on the probabilistic nature of arithmetic functions, and will bring therein the latest advances in geometric and harmonic analysis. Finally, homogenization and general multiscale stochastic analysis are ubiquitous tools in mathematical statistical physics, and their development is one of our primary interests.

An essential part of the CoE research is applications of cutting-edge mathematics in physical sciences as well as to statistics. Particular goals of the CoE include mathematical modelling of rock structures in view of applications to geothermal energy and improvement of the predictive accuracy of coagulation-fragmentation models in our pioneering work on "atmospheric mathematics", as well as development of stochastic algorithms applied in machine learning.