Three new professors of mathematics to start at the University of Jyväskylä
Mathematics has been studied for thousands of years. Mathematical research is often decades ahead of its applications, either directly in technologies, such as 5G networks or machine learning, or indirectly as an intermediate step in other sciences, such as physics. Society requires technology developers, basic scientists and especially applied researchers with a mathematical background, who can apply the more theoretical results in practice.
Professor Tapio Rajala: Research opens doors to various areas of application
Professor of Mathematics Tapio Rajala has been educated at the University of Jyväskylä. He earned his doctorate from JYU in 2009 and spent 2010 to 2012 as a postdoctoral researcher at the Scuola Normale Superiore in Pisa, Italy. He returned to the University of Jyväskylä as a postdoctoral researcher funded by the Research Council of Finland. In addition, he has received Academy Research Fellowship funding from the Council. Since 2020, he has worked as an associate professor at the University of Jyväskylä and will begin as the Head of the Department of Mathematics and Statistics on 1 August 2025.
Rajala conducts basic research in mathematical analysis. His areas of interest are optimal mass transport and Sobolev extension domains. Optimal mass transport has applications in a wide range of data processing applications, including image processing, machine learning, and economics. Rajala’s research also has links to information theory.
“Optimal mass transport investigates how the minimum cost transfers between two or more mass distributions are determined by a cost function, and what properties these minimisers and the broader structures they form have,” says Rajala explains.
In the study of Sobolev extension domains, the fundamental question focuses on identifying the subsets of space on which a Sobolev function can be defined in order for it to be extended to the whole space as a Sobolev function without increasing the norm by more than a constant factor.
“The extension domains are visible in many other areas of mathematics, for example, in the theory of partial differential equations,” says Rajala.
Professor Mikko Parviainen: Game theory behind many research fields
Professor of Mathematics Mikko Parviainen graduated from the Helsinki University of Technology (Aalto University) with a PhD in engineering in 2007. He started at the University of Jyväskylä in 2011. Since 2020, Parviainen has worked as an academy research fellow and served as an associate professor at the University of Jyväskylä. Starting from August, he will also work as the deputy head responsible for research and innovation activities in mathematics and statistics. Parviainen also gained international experience in the United States, serving as a visiting researcher at the University of Pittsburgh from 2008 to 2009. He has additionally held visiting researcher positions at the Mittag-Leffler Institute in Stockholm on three separate occasions.
Professor Mikko Parviainen conducts research on nonlinear partial differential equations and their connection to stochastic game theory, which is a relatively new area of research.
“Stochastic game theory provides a perspective which can be considered quite surprising. Using this perspective has, for example, provided proofs of the theory of partial differential equations by constructing strategies to suit players,” Parviainen explains. “This differs significantly from the traditional approach to partial differential equations.”
The connection between partial differential equations and stochastics has several applications, for example, in option pricing and portfolio management.
“Above all, the connection has also been important in several breakthroughs in pure mathematics,” says Parviainen. “The connection thus offers a new perspective on different areas of mathematics and powerful tools for mathematical research”.
He aims at further developing the stochastic game theory as well as the theory of nonlinear partial differential equations.
“My goal is to specifically expand the theory to certain types of graphs,” explains Parviainen. “The results obtained through graphs can also be interpreted in the context of machine learning. I want to develop theoretical methods that are general enough to cover a wide variety of examples.”
Partial differential equations also have many other applications, for example, in various fields of engineering and physics.
“The equations are used to model both heat conduction and wave motion, as well as in electromagnetism,” says Parviainen. “In addition, partial differential equations are needed in both control theory and, for example, in aircraft design.”
Vesa Julin – Aiming at a deeper understanding of nature
Professor Vesa Julin earned his PhD in mathematics from the University of Jyväskylä in 2010. Even before completing his PhD, Julin worked as a visiting researcher at the University of California. After completing his doctoral degree, he continued his career as a postdoctoral researcher at the University of Naples. He has also worked as a postdoctoral researcher and an Academy Research Fellow at the Research Council of Finland. Since 2020, Julin has been an assistant professor at the Department of Mathematics and Statistics at the University of Jyväskylä. He was awarded the Väisälä Prize by the Finnish Academy of Science and Letters in 2022.
Julin’s area of expertise is pure mathematics. His goal is to study mathematical models that represent natural phenomena. The research has focused on nonlinear partial differential equations, such as mean curvature flows, but also on isoperimetric inequalities, creating new connections between mathematical analysis and geometry.
The aim of Julin’s research is to understand nature, rather than to search for applications. Recently, he has been researching flow dynamics, such as the Euler and Navier–Stokes equations.
“My research problems often arise from the natural sciences, such as Euler’s formula, which describes the behaviour of liquids and gases, such as water and air,” says Julin. “I conduct research, for example, on a water droplet in zero gravity. If no external force is applied to the droplet, it remains spherical. However, when disturbed by an external force, it begins to vibrate irregularly and may eventually split into smaller droplets. This is a stability problem related to the isoperimetric problem, which has applications beyond mathematics, for example, in material science.”
