Mathematics is everywhere – mathematician Leila Taghizadeh
Leila Taghizadeh finds mathematics infinitely beautiful and uncertainties do not bother her at all. In her research, she uses mathematical methods to get to grips with them. How? By modeling uncertainties using tools from numerical analysis, probability theory and statistics.
For her current research project, "Computational Uncertainty Quantification in Nanotechnology", she received the prestigious Elise Richter Fellowship from the Austrian Science Fund FWF. She has just taken up the fellowship and returned to Vienna – after two years at the Technical University of Munich, opens an external URL in a new window – to the Institute of Analysis and Scientific Computing, opens an external URL in a new window at TU Wien. In our interview, she provides insights into her life as a researcher.
Ms. Taghizadeh, what is it like for you to return to Vienna and what is it like for you to work repeatedly in different countries?
Leila Taghizadeh: I feel at home in Vienna now as I have returned to my family. It is important for a researcher to change their working location and country to collect more experience. Of course, it is challenging to move, especially if you have a small child, but I decided at some point to do that, and I am happy since I gained valuable experience that I might not have obtained if I had not gone abroad. I thank my family for supporting me during the past two years.
What made you want to become a mathematician?
L.T.: Mathematics was my favorite subject at school. I always enjoyed solving mathematical problems in different ways; I was never bored. So I wanted to get more involved with it, and that's why I decided to study mathematics. Later I saw that the traces of mathematics are everywhere: in physics, biology, medicine, etc. Mathematics has the ability to describe natural phenomena, it is very comprehensive and that is also the beauty of it. Mathematics has an enormous impact on our lives!
You have just started your research on "Computational Uncertainty Quantification in Nanotechnology". How would you describe uncertainty quantification in simple terms?
L.T.: Uncertainty is everywhere in the sense that mathematical model parameters are usually unknown and can be random. They cannot be calculated or measured, so we need some tools to measure these uncertainties first, which is the primary goal of Uncertainty Quantification. The ultimate goal is to reduce the uncertainties of mathematical models in order to find the model solution or model unknowns as accurately as possible. My research deals with quantifying and reducing the uncertainties in mathematical models in computational science and engineering, in particular for mathematical models of nanoelectronic devices.
How can we imagine the set-up of a mathematical experiment and why are such experiments expensive?
L.T.: Physical or biological phenomena are usually described by mathematical models, in particular by systems of partial differential equations (PDEs). A comprehensive knowledge of the mathematical model gives us a qualitative and quantitative understanding of the phenomena. For this, we need to look at the corresponding inverse problem as well, where experimental data can help by updating our prior knowledge about the model unknowns. An experiment, physical or biological, can be delicate or expensive to set up or to perform, for example, experiments at the nanoscale. On the other hand, from a mathematical point of view, this can be expensive in terms of the number of PDE solves.
What will happen with the results of your work and what impact might they have?
L.T.: My research focuses on the uncertainty quantification and optimal experimental design of mathematical models in computational science and engineering. The results include optimal conditions and an experimental set-up under which most information can be extracted from the measurement data. This is important in many aspects; the crucial impact is that applying the optimal designs reduces the uncertainty of the model unknowns, which leads to more accurate statistical (Bayesian) inversion results. In one word, the goal is to reduce the uncertainty of the mathematical model for an optimal and robust design of experiments and devices.
Thinking back, what was important to your career? Did you know what you wanted to be when you were a child, and were you influenced or encouraged by your family?
L.T.: Since I was a child in school, I was encouraged all the time by my family, especially my father. He reminded me from time to time on my future and goals, and that I should work hard now in school and later at university to achieve them. I think what is important to a future career is hard work at the point where we are now. This needs motivation and hope, of course; I will never forget the continuous and endless influence and encouragement of my husband in this way.
What advice do you give to young scientists?
L.T.: My advice to young scientists is to work hard, do your best, and never give up. There will always be good and even disappointing suggestions and advice from different people around you; it is you that should distinguish between good and bad advice; take the good ones and let the disappointing ones go.
Thank you for the interview!
Leila Taghizadeh studied mathematics in Iran, where she initially also worked as a university lecturer. In 2012, she moved to Austria to work at the Institute of Analysis and Scientific Computing at TU Wien - first as a software developer, then as a project assistant. In 2019, she completed her PhD on uncertainty quantification, for which she received the Hannspeter Winter Award in 2020. After about two years PostDoc at TU Wien, she moved to Germany in 2021 as a postdoctoral researcher at the Department of Mathematics of Technical University of Munich.
In 2022, she was awarded an FWF-funded Elise Richter Fellowship for her project "Computational Uncertainty Quantification in Nanotechnology", which she started at the Institute of Analysis and Scientific Computing at TU Wien on May 15, 2023. This is the only FWF Elise Richter Fellowship granted for TU Wien in 2022, and the only one in Mathematics in Austria in 2022.
Interview: Edith Wildmann