What are your research topics?
I study mathematical models, which can describe, among other things, natural phenomena and specifically their temporal variation. With my colleagues, I strive to understand how solutions gained through models behave, how they depend on the variables used and which details of the models are relevant to the phenomenon being investigated.
Through our research, we are developing both models and the predictability of the characteristics of related solutions.
Where and how does the topic of your research have an impact?
One of the models we have been studying the most illustrates thermal conductivity and energy transport in lattice systems, something found, for example, in electronics. The concepts centrally associated with this research include randomness and stochastic temporal variations. Then again, the same methods are also suited to modelling stock markets. In fact, some of our research findings are concerned with the mathematical structure of stock market models.
In addition to randomness, my research involves non-linear factors, which can result in sudden changes to the solutions produced by a model that are difficult to predict. Recently, we launched a collaborative project between research groups specialising in physics and mathematics in which we aim to improve a model describing changes in the atmosphere. Improvements in predictability are needed in this field when assessing the impact of various climate change scenarios.
What is particularly inspiring in your field right now?
Researchers have recently developed novel methods and gained new results that could help in modelling various everyday phenomena, such as thermal conductivity. I am interested in finding out whether this could lead to a mathematical basis for thermal conductivity models and for the theory related to them.
Jani Lukkarinen is the professor of mathematical physics at the Faculty of Science.
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