The Department of Mathematics and Statistics has proved to be a stimulating research environment for several subjects of mathematical and statistical study and the members of our community from students to senior researchers constantly produce results of the highest international level. Active research is reflected in a variety of activities: publications, meetings, and participation in academic societies.
The department is a partner in the Research Council of Finland Flagship of Advanced Mathematics for Sensing (FAME) and coordinating the Research Council of Finland Center of Excellence in Randomness and Structures (FiRST).
FAME – Flagship of Advanced Mathematics for Sensing, Imaging and Modelling is a multidisciplinary competence centre harnessing applied mathematics for the benefit of industry, environment and society.
The Centre of Excellence in Randomness and Structures (FiRST) brings together leading mathematicians in Finland to collaborate towards the advancement of the common research themes of randomness and structures. The CoE aims at mathematical development at the crossroads between probabilistic methods, quantum and conformal field theory, geometric and harmonic analysis, partial differential equations and analytic number theory. The Centre’s specific goal is to understand the analytical and geometric characteristics of random structures.
The Department of Mathematics and Statistics regularly organises seminars and colloquia open to all. The events deal with the Department’s latest research findings and interesting trends in our fields of research.
Mathematical research at the Department of Mathematics and Statistics is conducted by internationally leading groups in inverse problems, mathematical analysis, mathematical physics, and mathematical logic. They combine methods from probability, geometry, partial differential equations, and modern mathematical logic. The research questions range from imaging, randomness, complex analysis, dynamics, and number theory to questions in second order logics.
The members of the group Geometric Analysis and Quasiconformal Geometry have broad interests in analysis and geometry. Active research topics include quasiconformal analysis and partial differential equations related to differential and Riemannian geometry, topology, and applications. The research of the group is funded by the Center of Excellence FiRST of the Research Council of Finland.
Mathematical logic lies at the intersection of mathematics and logic: it uses mathematical methods to analyze logical systems, and uses logical frameworks to study mathematics and other formal disciplines. The field investigates the relationship between formal languages and mathematical structures, with applications across philosophy, computer science, linguistics, and mathematics. Current research in the Helsinki Logic group focuses on logics in team semantics, finite model theory, logic in computer science, model theory, and set theory.
Modern mathematical physics was born from the attempts to gain mathematical understanding of quantum field theory and statistical mechanics. In those fields powerful new methods were developed around the concepts of renormalization and universality. The Helsinki Mathematical Physics Group has been in applying these ideas to a wide variety of problems including turbulence and stochastic differential equations, kinetic theory, fluctuating thermodynamics (classical and quantum), Stochastic Löwner Evolution (SLE), scaling limits of two dimensional critical lattice models and Liouville Quantum Gravity.
Our group's research deals with several mathematical problem areas that involve probabilistic questions in various setups. These include probabilistic methods in mathematical physics, analysis and geometry as well as some probabilistic analytic number theory. Further topics include probabilistic algorithms, especially Markov Chain Monte Carlo methods.
Inverse problems research lies at the intersection of pure and applied mathematics. The forward problem corresponding to an inverse problem is usually a well defined problem in physics, engineering or medical imaging. What is inverted in an inverse problem is the causality: Whereas in a forward problem we start from the causes and end up with the results, in an inverse problem we start with partial knowledge of the causes and the result and infer more about the causes. Important application areas of inverse problems include medical imaging, nondestructive testing and seismic prospecting.
The Mathematics Education Research Group studies mathematical flexibility and mathematical misconceptions. The master’s theses of students completing studies for subject teachers in mathematics often investigate and analyse errors and misconceptions found in student answers to the mathematics test of the Finnish matriculation examination. Mathematical flexibility refers to the ability to apply different methods for solving and presenting mathematical problems based on their structure and nature. The group’s current major project focuses on the effect of such flexibility on a smooth transition from primary to lower secondary education in mathematics.
Research in statistics at our department is highly collaborative, spanning multiple disciplines to generate integrated knowledge that benefits both science and society. Our statistical research methodologies adapt to meet the demands of evolving challenges, incorporating knowledge from various fields to develop rigorous methods for insightful statistical inference.
We aim to understand how ecological and environmental processes shape the world we live in. For this, we work in the interface of ecology, environmental sciences, and statistics. Our research interests span from statistical methods development to ecological research and environmental sciences. We also actively apply our research to more applied questions such as environmental management and risk assessment. We work at the Organismal and Evolutionary Biology Research Program (Faculty of Biosciences and Environmental Sciences) and at the Department of Mathematics and Statistics (Faculty of Science).
Eng: Regression and time series analysis -group develops the theory of data based statistical models and applies them in empirical problems. Researchers in the group develop and apply e.g. standard and robust estimators and tests in multivariate methods, regression models, and time series models. The analyzed datasets may also be high-dimensional datasets, where there are more variables than observations.
Uncertainty is an inherent part of all scientific activity and the generally agreed framework for handling uncertainty is the use of probability. Our lab focuses on enabling and making inferences with the aid of probabilistic models, with a focus on evolutionary epidemiology of bacterial infectious diseases but also within a wider range of applications in life sciences, technology and engineering. We are part of the ELLIS Institute Finland and have coordinated development of the
Our work combines a thorough understanding of statistical modeling with real life experience on what works in practice. We develop and apply multidimensional statistical models that connect observed characteristics, such as disease susceptibility, to genome information. We also study what the current distribution of genetic variation can tell about our past.
Our group works extensively with time to event data arising at various stages of life. We specialize in handling heterogeneous data possibly arising from different sources and under varying observation schemes. Our expertise is in going beyond the obvious from the data.
The research group focuses on the development of statistical methodology for multivariate and high-dimensional data. Research topics include dimension reduction, robust methods, and statistical analysis of spatial and temporal data, with applications across environmental sciences, biology, medicine, and other data-intensive fields.