Satunnaisuuden ja rakenteiden huippuyksikkö (FiRST)
Päärahoittaja
Rahoittajan antama koodi/diaarinumero: 346310
Päärahoittajan myöntämä tuki (€)
- 270 767,00
Rahoitusohjelma
Hankkeen aikataulu
Hankkeen aloituspäivämäärä: 01.01.2022
Hankkeen päättymispäivämäärä: 31.12.2024
Tiivistelmä
Summary:
Our proposal brings together leading mathematicians in Finland, including a new generation of world-class experts, to collaborate towards the advancement of the common research themes of "Randomness and Structures." Each of the three previous ICM's has seen one of our PI’s as an invited speaker, and we are in a unique position worldwide, with our combined strengths perfectly fitting our common tasks.During the past years, in a wide range of important problems in pure and applied contemporary quantitative sciences, the role of the probabilistic point of view has become increasingly important. A notable example of this is random geometry, a new, vibrant field which studies random geometrical objects that arise in classical and quantum statistical physics. Our teams have been at the forefront of the mathematical developments at the crossroads between probabilistic methods, quantum and conformal field theory, and geometric and harmonic analysis, which have made Finland a major international center in random geometry. Moreover, 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 harmonic analysis. Finally, homogenization and general multiscale stochastic analysis are ubiquitous tools and their development is one of our pivotal interests.An essential part of our proposal comprises applications of cutting edge mathematics, building on our joint expertise and past experience. This includes functional data analysis methods together with development and analysis of automatic probabilistic algorithms, which we also envisage to apply in probabilistic machine learning and its uses in the construction of numerical solution of rough PDEs. Another key research goal is the mathematical modelling of rock structures in view of applications to geothermal energy.We will also continue our pioneering work on 'atmospheric mathematics'. One particular goal is in significant improvements of the predictive accuracy of coagulation-fragmentation models.We shall sustain and develop researcher training in our fields. Emphasizing a broad background and open mindedness.
Our proposal brings together leading mathematicians in Finland, including a new generation of world-class experts, to collaborate towards the advancement of the common research themes of "Randomness and Structures." Each of the three previous ICM's has seen one of our PI’s as an invited speaker, and we are in a unique position worldwide, with our combined strengths perfectly fitting our common tasks.During the past years, in a wide range of important problems in pure and applied contemporary quantitative sciences, the role of the probabilistic point of view has become increasingly important. A notable example of this is random geometry, a new, vibrant field which studies random geometrical objects that arise in classical and quantum statistical physics. Our teams have been at the forefront of the mathematical developments at the crossroads between probabilistic methods, quantum and conformal field theory, and geometric and harmonic analysis, which have made Finland a major international center in random geometry. Moreover, 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 harmonic analysis. Finally, homogenization and general multiscale stochastic analysis are ubiquitous tools and their development is one of our pivotal interests.An essential part of our proposal comprises applications of cutting edge mathematics, building on our joint expertise and past experience. This includes functional data analysis methods together with development and analysis of automatic probabilistic algorithms, which we also envisage to apply in probabilistic machine learning and its uses in the construction of numerical solution of rough PDEs. Another key research goal is the mathematical modelling of rock structures in view of applications to geothermal energy.We will also continue our pioneering work on 'atmospheric mathematics'. One particular goal is in significant improvements of the predictive accuracy of coagulation-fragmentation models.We shall sustain and develop researcher training in our fields. Emphasizing a broad background and open mindedness.
