Welcome on boardResearch of random dynamical systemsProf. Dr. Vitalii Konarovskyi joins the Department of Mathematics

14 May 2024, by Heiko Fuchs

Photo: privat

Prof. Dr. Vitalii Konarovskyi

Every year, numerous new researchers join the University of Hamburg. In this series, we introduce them and their fields of research. This time: mathematician Prof. Dr. Vitalii Konarovskyi.

Prof. Dr. Vitalii Konarovskyi came to Hamburg from Bielefeld University in the winter semester and took up the W2 professorship for "Mathematics, in particular Stochastic Processes and their Applications" at the Department of Mathematics in the Faculty of Mathematics, Informatics and Natural Sciences.

Mr. Konarovskyi, what are your research topics?

I study stochastic processes that are the key mathematical tool for modelling complex evolving systems that appear in physics, biology, computer science and many other disciplines. They are used, for example, to describe the spread of epidemics, the diffusion of gas molecules and the training of neural networks.

What exactly are you working on?

My main research is at the intersection of four different directions that have developed over the past ten years: These are singular stochastic partial differential equations, stochastic flows, optimal transport in mathematics and the statistical non-equilibrium mechanics of materials in physics as well as engineering. Recently I also started a few projects in mathematics for machine learning and random graph theory.

Where can your work be applied?

For example, I investigate a class of random graphs, called stochastic block model, that can be used for the description of the spread of infections in the population in epidemiology or the formation of clusters in networks in computer sciences. Together with my co-authors we proposed a new type of stochastic (partial) differential equations that can be used for training and investigating neural networks in machine learning.

What are your plans at the Universität Hamburg?

My main goal at the Universität Hamburg will be to build a strong group focusing on stochastic processes and their application that would work closely with different research groups in physics, biology and computer science. In particular, I will focus on joint work with researchers from physics to construct and study mathematical models that arise in particle physics, hydrodynamics, climate research and other fields.

What do you need for your research?

For my work, I usually only need a pen and some notebooks to write down my computations. Of course, I also need a bit of luck to find the right ideas and implement them mathematically correctly.

Why did you choose the Universität Hamburg?

Hamburg is a very good place for me because of the many opportunities for cooperation. There are many excellent groups working in physics and earth system sciences, computer sciences, etc., that deal with topics that can be combined with my research, such as particle physics, climate research or machine learning. In addition, I have already worked at the Universität Hamburg as a substitute professor and find it very nice to come back and continue my work.

What are you planning for your courses?

Due to their wide range of applications, the concepts of stochastics are not only of great importance for students of mathematics, but also for other subjects. I would therefore like to offer interdisciplinary courses for students from different subject areas. I already started implementing this idea as a substitute professor at the Universität Hamburg in 2020/2021, when I offered the seminar "Application of large deviations to statistical mechanics" for students of mathematics and physics. At that time, however, it was more of an experiment. Now I would like to systematically deepen the education of students of physics, computer science, biology and other subjects in the most important concepts of stochastic processes and related fields.