About

Many problems in mathematics and its multifarious applications lead to strikingly similar - universal - questions pertaining to random structures. The geometry of random structures is often fractal. Such structures occur particularly in statistical and quantum field theory, with magnetisation and quantum gravity as examples.

The Centre of Excellence in Randomness and Structures investigates such phenomena. The Centre’s specific goal is to understand the analytical and geometric characteristics of random structures. As this research requires expertise in a number of mathematical fields, the Centre of Excellence will bring together a new generation of leading mathematicians to solve these problems.

Random structures also make an unexpected appearance in number theory, including the structure of the sequence of prime numbers. As the noted mathematician Paul Erdős stated: "God may not play dice with the universe, but something strange is going on with the prime numbers." Among other things, the Centre of Excellence explores the random nature of multiplicative functions and the Riemann zeta function.

The Centre will also develop new analytical and geometric methods aimed at understanding, for example, how macroscopic laws of nature follow from microscopic ones. Prospective applications of fundamental importance are in atmospheric (e.g. aerosol particle condensation) and lithosphere (e.g. water percolation in rocks) physics.
The Centre of Excellence also conducts research aimed directly at producing applications by developing high-dimensional statistics as well as randomised algorithms and their geometric understanding for the purposes of computational applications and machine learning.

The Centre of Excellence in Randomness and Structures is headed by Professor Eero Saksman. In addition to the University of Helsinki, the research groups comprising the Centre of Excellence are active at Aalto University, the University of Jyväskylä and the University of Turku.
Our research

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.
Prizes

Associate Professor Eveliina Peltola

2027 - Conference “Dynamics, Equations and Applications (DEA)” (Keynote speaker), Kraków, Poland

2026 - Chaire Jean Morlet

2025 - The 2025 ANZAMP Meeting, University of Melbourne, Australia (plenary speaker)

2025 - Finnish Academy of Science and Letters (Tiedeakatemia) Lifetime Membership

2024 - Väisälä Prize

2023 - Nordic Congress of Mathematicians, Aalborg, Denmark (plenary speaker)

2023 - “Physics@Veldhoven”, Netherlands (invited session speaker)

2022 - Nordic Congress of Mathematicians, Espoo, Finland (session speaker)

2021 - 10th World Congress in Probability and Statistics (Bernoulli), Seoul, Korea (session speaker)

2020 - Finnish Mathematical Days / Matematiikan päivät 2020, Oulu, Finland (plenary speaker)

2019 - Stochastic Processes and their Applications (SPA), Invited Session, Northwestern University, US

2018 - International Congress of Mathematical Physics (ICMP), Equilibrium Statistical Mechanics Session, Montreal, Canada

2016 - Outstanding Doctoral Dissertation Award (Faculty of Science of the University of Helsinki)

2013 - Ernst Lindelöf Master’s Thesis Award

2013 - Distinguished Dissertation Award (Faculty of Science of the University of Helsinki)


Professor Matti Vihola

2021 - Ellen and Artturi Nyyssönen Foundation award

2011 - The Rolf Nevanlinna Research Foundation prize

2010 - The Finnish doctoral thesis in Mathematics prize 
 

Professor Tuomas Hytönen

2022 - of the Finnish Society of Sciences and Letters

2017 - of the International Society for Analysis, its Applications and Computation

2016 - Plenary speaker at the 27th Nordic Congress of Mathematicians

2014 - Invited speaker at the ICM (International Congress of Mathematicians)

2013 - of the Finnish Academy of Science and Letters


Professor Tuomo Kuusi

2026 - Invited speaker at the ICM (International Congress of Mathematicians)