"Both at HSE and l'X, we apply algebra to research differential equations, but that's where the similarities end"

This summer, Alexander Demin, a student of Applied Mathematics and Information Science programme, interns at École polytechnique. We talked to him about his research, France and his studies at HSE University:

I'm a third-year student of the Applied Mathematics and Information Science programme. My specialisation is machine learning, but my range of interests includes many areas relevant to computer science, such as computer algebra and numerical computing.

I can't say that I chose the Faculty of Computer Science after mature deliberation. In the 11th grade of high school, I went to the Open Day of the Faculty, browsed its website, and was moved by the approach to studies at HSE University. Moreover, my teachers and friends advised me to consider this programme, so I chose it.

HSE University

Last year at HSE University, a colleague and I did a project supervised by Professor Gleb Pogudin, of École polytechnique. The project was on the application of exact sparse linear algebra to the study of differential equations models. I have been analysing differential equations that arise in applied molecular biology problems and have been trying to reduce their dimensionality while retaining the basic parameters of the system. This dimensionality reduction can help to learn more about a complex model of a biological process from its reduced, relatively simple version.

We have devised a practical algorithm that is guaranteed to find the reduction of the system, if it exists at all, and hope to write an article about it.

Internship

A colleague found an internship at École polytechnique (or l'X, as it is affectionately known) in a Telegram channel and shared it with me (thanks, Lisaveta!). It was sad that I didn't fit the formal criteria and had no lab experience. I'm glad I decided to give it a try anyway.

For the application, I had to submit the standard documents: CV, motivation letter, and letters of recommendation. In addition, HSE University cooperates with École, and I was nominated for this internship by the Faculty. 

I am very grateful to the HSE University teachers who wrote my letters of recommendation. I would also like to express my enormous gratitude to the external communications unit of the Faculty and personally to Sergey Karapetyan for his help with everything from my application questions to the grammar in my motivation letter (which I spent three weeks writing, although it was only one A4 page). 

The internship is related to my research at the Faculty in the topic rather than approach. Both at HSE and l'X, we apply algebra to research differential equations, but that's where the similarities end. The work format also differs: at the Faculty I worked online with a colleague, whereas in Paris I sometimes go to the lab and try to do everything myself.

My supervisor in France is also Professor Gleb Pogudin. 

I study the identifiability of the parameters of differential equations systems. In other words, we are trying to answer the following question: is the parameter identified uniquely in the system of equations?

Despite the analytical form of the problem, the question of the identifiability of the parameter is reduced to checking some of its algebraic properties. Therefore, the work is based on computer algebra such as rational interpolation, Gröbner bases, and modular computation.

École Polytechnique

I'm an intern at LIX, a large laboratory of the Inria and CNRS research institutes. It is located in the Alan Turing Building. It hosts about a dozen teams of scientists from a wide variety of fields. It also has a strong presence in areas such as cryptography or formal verification, which are not very popular at the Faculty of Computer Science.

The group I'm in is called Modélisation algébrique, and it's made up mostly of École professors doing computer algebra. The atmosphere in the lab is very friendly and unhurried in the French way, and it's a real pleasure to work.

Coming to France was quite easy: there were no serious travel restrictions from Russia at the beginning of summer, and they gave me a visa a couple of days before departure. I had to be a little bit sad about the quarantine and the PCR tests, but all in all, I got off easy. Some students from Russia had a bit less luck: they were either denied a visa several times or had to fly to France via another country.

I stayed at the École campus near Paris, near Palaiseau. It's a nice village with bakeries, bars, friendly townspeople, and houses painted in warm colours - everything is as one would expect in a European village. 

The campus is home to several Paris universities and laboratories combined into one big Institut Polytechnique de Paris. I still haven't been able to get around it in its entirety. In general, I really enjoyed travelling around France: the sombre castles and pirate towns of the north coast, the sunny Nice and Cannes of the south. Verweile doch! Du bist so schön!