Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Mathematics has many faces but everything eventually fits together like a puzzle

Dr. Hana Šmitala Mizerová works on the numerical analysis of models of fluid, liquid and gas flows that occur in many natural phenomena. Hana Šmitala Mizerová was the only researcher of Comenius University Bratislava to win the 2022 L'Oréal - UNESCO For Women in Science Award in the category of formal science. Alongside her, Xiaolu Hou from the Slovak Technical University in Bratislava received the award in the category of engineering sciences and technologies, and Soňa Kucharíková from the University of Trnava won in the category of life sciences, including environmental sciences. They shared 15,000 euros, which they can use towards their scientific research and other goals. In this interview, she told us more about her work.

17. 03. 2023 09.18 hod.
By: Naša univerzita magazine staff

You are a laureate of the formal sciences category in the L'Oréal – UNESCO For Women in Science program. What does this award mean to you and how do you view it?

Receiving the award was, of course, a great pleasure and I am very grateful for it. I am glad that this talent program specifically supports young female researchers, who are still underrepresented in technical sciences.

Why did you sign up to the competition?

I learned about the project from our dean while I was still on parental leave. It was already coming to an end, so I saw joining this program as a possible restart of my career. And also as an opportunity to bring my work closer to the public and to attract new students to mathematics.

Have you received any other awards? Which of them make you the most proud?

I have only been doing research for a relatively short time and the L'Oréal - UNESCO Women in Science award is my first major award. At the beginning of my career, I was greatly encouraged to do research by winning the prize of the Faculty of Physics, Mathematics and Informatics of the Johannes Gutenberg University in Mainz for an excellent dissertation.

Did you know from early on that mathematics was what you wanted to do in the future?

I remember that I liked logical problems and puzzles even as a child and math at school was one of my favourite subjects. However, I only decided to study mathematics in the graduation year of my secondary school. Until then, I considered studying foreign languages or medicine. What led me to choose the study at the Faculty of Mathematics and Physics of Comenius University was curiosity, I think. I didn't know what was in store for me and I had no idea that research in mathematics would become my profession.

In your research you focus on mathematical models of the flow of fluids, liquids and gases that occurs in many natural phenomena and engineering applications. Could you tell us more about this area and what practical applications your research has?

I work specifically on Navier-Stokes equations that model the flow of fluids. They have a very wide range of practical applications, from meteorology to car aerodynamics, medicine and astrophysics. It is a system of partial differential equations, whose solutions are functions describing the changes in density, velocity and total energy of the fluid in time and space. However, in general, we cannot find their analytical solution, and we therefore need suitable numerical methods that allow us to design computer algorithms which generate an approximate calculation. To make sure that these simulations do not rely solely on a numerical method which provides a solution that is only apparently correct, we must verify its correctness and accuracy with a mathematical proof of the convergence of the approximate solutions and, and we must estimate the error. These theoretical results are then used in applied research, where experts deal with practical problems from real life.

Dr. Hana Šmitala Mizerová
studied mathematical analysis at the Faculty of Mathematics, Physics and Informatics of Comenius University Bratislava, continued her doctoral studies in mathematics at the Johannes Gutenberg University in Mainz and Waseda University in Tokyo as part of a three-year scholarship awarded by the German DFG agency. She also worked as a researcher at the Institute of Mathematics of the Czech Academy of Sciences. In 2021, she obtained the qualification of independent researcher (VKS IIa). She currently works at the Department of Mathematical Analysis and Numerical Mathematics of the Faculty of Mathematics, Physics and Informatics. Her field includes numerical analysis of the Euler and Navier-Stokes equations that describe fluid flow.

What is your role in this research?

My role is to design and analyse numerical methods that are used to solve problems involving the flow of liquids and gases. Ocean surface motion requires a different approach than does airflow around the wing of an aeroplane. Me and my colleagues study which methods are effective and stable for a specific problem, and try to find out whether the sequence of solutions they provide converges; which solution is the limit of this sequence, or what error a numerical calculation produces.

How long have you been doing research?

I started researching Navier-Stokes equations and fluid flow back in 2009 while writing my bachelor's thesis. I then continued to study this area in my diploma thesis and my dissertation. In recent years, I had the opportunity to collaborate on the design of a new approach in the numerical analysis of compressible fluids. We would like to expand this approach to include models that take into account the interaction of the fluid with its surroundings, i.e. the influence of the external environment, such as an external heat source. Imagine a pipe in which the fluid flows periodically, i.e. so that inflow at one end is the same as outflow at the other. Our recent theoretical results of numerical solutions can be applied to such situations. Our next goal is to see if these results remain valid if, for example, the fluid begins to flow into the pipe faster or the pipe heats up due to solar radiation.

What do you enjoy most about working as a research mathematician?

What I enjoy the most about mathematics is that it offers many possibilities of describing and exploring the world around us. To me, it is fascinating how numerical calculations and theoretical proofs show the precision with which mathematics reflects the laws of physics. Mathematics is diverse and in a sense it gives the freedom to choose one's own research career. On the other hand, it often requires working in your free time. This, however, is compensated by the satisfaction of solving a problem and seeing everything fit together like a puzzle.

Have you ever encountered any gender-based prejudice or misunderstandings on the part of your colleagues?

I personally have not encountered or witnessed any prejudice even though men still dominate the field of mathematics. Research work should not be judged by the author’s gender, but by its contribution to society.

What would you say to budding female researchers who want to pursue mathematics like you?

It is indispensable to like your work and be driven by curiosity and the desire to discover. I want to give them encouragement: don't be afraid to embark on a research career, even if you may not yet know what awaits you. In the beginning it is also important to have a good mentor to show you the possibilities and guide your first steps.


Radka Rosenbergová