‘Math is Beautiful’

Anna Kozhina, Research Assistant at HSE’s international Laboratory of Stochastic Analysis and its Applications

Photo courtesy of Anna Kozhina

Anna Kozhina, a Research Assistant at HSE’s international Laboratory of Stochastic Analysis and its Applications, earned her PhD at Heidelberg University in Germany with highest distinction and earned an academic degree of the first category  from HSE’s new Dissertation Committee. This year Anna’s dissertation was awarded the Wilma-Moser prize, which recognizes the best work among female graduate students in the natural sciences. In an interview with HSE News Service, Anna discussed what made her fall in love with mathematics and how science keeps her on her toes.

First Steps

My parents both have educational backgrounds in engineering. Thanks to them, math and the natural sciences didn’t intimidate me, even from a young age—if anything, they piqued my interest. Probably, what got me into math was my time in math class at School No. 91, where, at the time, there practical lessons of mathematical analysis were offered. Graduates of the school who had gone on to study at Moscow State University, the Moscow Institute of Physics and Technology, and other prestigious universities taught these classes, so we learned the basics from real experts. Their advice, experience and enthusiasm inspired me to pursue the subject area further.

Inspirational Science

Math is beautiful. That moment when an unwieldy illogical problem gives way to a bright idea is wonderful. And its practical applications are so diverse! It’s very important to be motivated in what you do.

Academic Career

Rather than a childhood dream, I was drawn to science by a specific project. I wanted to complete the research I started while working on my diploma with Professor Valentin Konakov, who was my supervisor at the Faculty of Mechanics and Mathematics at Moscow State University. My graduation from the university coincided with the opening of the laboratory at HSE, where Professor Konakov was appointed Laboratory Head and Chief Research Fellow. I then decided to continue my studies at the postgraduate level at HSE while working in the laboratory. I wanted to try an arrangement that would allow me to immerse myself in research 100%.

A Year of Great Achievements

In one year, I received a PhD from Heidelberg University and a degree from HSE. I signed a Cotutelle contract, which allowed me to combine programs at different universities. Under the terms of this agreement, I spent a total of slightly less than a half-term at Heidelberg and the rest of the time at HSE. First and foremost, you have to choose not a university or a city, but a topic and a supervisor. Professor Konakov had been working with Professor Mammen from Heidelberg University on a subject of interest to me for a long time, so my choice was obvious. But I’ll admit the very atmosphere of one of the oldest universities in Germany was a pleasant and beneficial addition to my research.

Together with our supervisors, we made up an alternating research schedule: I would spend half a year in Moscow and half a year in Germany. This allowed me, on the one hand, not to spend too much on travel, and, on the other, to remain in contact with both groups. In addition, I tried my hand at working as a teaching assistant for some HSE courses and gained pedagogical experience, which I consider to be an important part of postgraduate studies. Studying in Germany allowed me to include results I obtained at the University of Évry Val d'Essonne (Paris) under the supervision of Professor Menozzi in my dissertation.

'The Parametrix Method and its Applications in Probability Theory'

This was the topic of my dissertation. Its main idea was that, in trying to describe the world in models, we begin to use more complex versions of them, and, for example, add randomness to them. One of the methods of this modeling is to set the dynamics of the process we’re interested in by solving a certain equation in which there is noise. Sometimes such equations can be solved analytically using formulas, sometimes not. When they don’t, methods of approximate solutions can be used. My dissertation evaluated the extent to which similar schemes of approximate solutions can model unknown processes. One of the most common applications of this is in the analysis and forecasting of financial market prices.

Summa cum laude

At Heidelberg University, I received the highest distinction possible for my dissertation—I graduated summa cum laude. A dissertation defense in Germany is quite different from the usual procedure we have in Russia. There, besides receiving a positive evaluation of the dissertation itself, you have to pass the oral exam, which takes place right at the defense. After the presentation, everyone leaves the room except for the dissertation committee and the student. The PhD candidate then has to answer questions not only about the subject of his or her dissertation but also its counter argument. In my case, since my dissertation was on applied theory of probability, I had to answer questions about complex analysis. This procedure keeps you on your toes up until the very last moment of the defense, because you don’t only have to be able to structure your results well, prepare a talk, and orient yourself in your topic of inquiry, but you also can’t forget the general stuff that constitutes the ‘gentleman’s art’ of mathematics.

The Best of the Best

The Wilma-Moser Prize has been awarded at Heidelberg University to the two or three best dissertations written by female graduate students in medicine and the natural sciences since 2005. This year, it was awarded to me. The award ceremony will be held in June, in a large hall in the historic quarter of the university. To be honest, I almost missed the invitation to the ceremony—I didn’t pay attention to the general email, and it was hard to believe when I first saw it. Of course, it is nice to be acknowledged for work that you put so much time and effort into. I hope my example will help others to believe in themselves and know that science has no borders or national differences.

New Goals

At the moment, it is interesting to me to explore and develop the practical application of models. On the one hand, I do not think that the tasks of fundamental science should emerge exclusively from practical cases, but on the other hand, moving away from practice, there is a danger of heading towards a dead end. Now I have decided to work in the industry. I’ve been working for a year now in a department at Sberbank where I can put my acquired knowledge into practice.