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

2026

Eveliina Peltola -
Tuomo Kuusi - Invited speaker at the ICM (International Congress of Mathematicians)

2025

Christian Webb - European Research Council Consolidator Grant 2025-2030
Eveliina Peltola - The Finnish Academy of Science and Letters Lifetime Membership
Kaisa Matomäki - of the Finnish Society of Sciences and Letters
Tuomas Hytönen - Selected as for 2026-2031 term

2024

Eveliina Peltola -
Kaisa Matomäki - jointly with Maksym Radziwiłł, Terence Tao, Joni Teräväinen, and Tamar Ziegler
Xiao Zhong - The Finnish Academy of Science and Letters Lifetime Membership

2023

Eveliina Peltola - European Research Council Starting Grant 2023-2027
Eveliina Peltola - Nordic Congress of Mathematicians, Aalborg, Denmark (plenary speaker)
Kaisa Matomäki - jointly with Maksym Radziwiłł

2022

Tuomas Hytönen - of the Finnish Society of Sciences and Letters

2021

Christian Webb -
Eero Saksman - The Royal Norwegian Society of Sciences and Letters: member 2021-
Kaisa Matomäki - in Mathematics
Matti Vihola -
Tuomo Kuusi - The Finnish Academy of Science and Letters Lifetime Membership

2020

Kaisa Matomäki -
Pauliina Ilmonen -

2019

Kaisa Matomäki - The Finnish Academy of Science and Letters Lifetime Membership
Kaisa Matomäki - jointly with Maksym Radziwiłł
Tuomo Kuusi - European Research Council Consolidator Grant 2019-2023
Tuomo Kuusi -

2018

Eero Saksman -
Eero Saksman -   and the Silver Onsager Medal and at the Norwegian University of Science and Technology 
Jani Lukkarinen -
Kaisa Matomäki - Invited speaker at the International Congress of Mathematicians (jointly with M. Radziwill)

2017

Tuomas Hytönen - The Finnish Academy of Science and Letters Lifetime Membership
Tuomas Hytönen - of the International Society for Analysis, its Applications and Computation

2016

Eveliina Peltola - Outstanding Doctoral Dissertation Award (Faculty of Science of the University of Helsinki)
Kaisa Matomäki -
Kaisa Matomäki - for Scientific Courage
Kaisa Matomäki - jointly with Maksym Radziwiłł
Tuomas Hytönen - Plenary speaker at the 27th Nordic Congress of Mathematicians

2014

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

2013

Eero Saksman - of the Finnish Society of Sciences and Letters
Tuomas Hytönen - of the Finnish Academy of Science and Letters

2012

Pekka Koskela -

2011

Matti Vihola - The Rolf Nevanlinna Research Foundation Prize
Tuomas Hytönen - European Research Council Starting Grant 2011-2016
Xiao Zhong -

2010

Matti Vihola - The Finnish doctoral thesis in Mathematics prize 
Pekka Koskela - Invited speaker at the ICM (International Congress of Mathematicians)

2009

Jani Lukkarinen - Invited talk at XVI International Congress on Mathematical Physics (ICMP09)
Pekka Koskela - Selected as Research Council of Finland Academy Professor for 2010-2014 term

2007

Eero Saksman - The Finnish Academy of Science and Letters Lifetime Membership
Eero Saksman -

2005

Pekka Pankka - Suomen matemaattisen yhdistyksen väitöskirjapalkinto 2005

2004

Pekka Koskela - The Finnish Academy of Science and Letters Lifetime Membership

2001

Pekka Koskela -

2000

Pekka Koskela - Invited speaker at the third European Congress of Mathematics 

1994

Eero Saksman - The Nevanlinna prize for best Finnish mathematics dissertation