From cryptography to space flight control: what leading Russian mathematicians were doing in 2022

The improvement of computational methods, the creation of new models and algorithms allow scientists to solve problems in various fields far beyond mathematics itself – from space to the chemical industry. As part of the national project “Science and Universities”, the Russian Ministry of Education and Science continues to support a network of mathematical centers: four world-class mathematical centers (MCMU) and eleven regional scientific and educational mathematical centers (NOMC). Their priority task is to maintain and strengthen Russia’s leading positions in the field of mathematical sciences by conducting fundamental and applied research, as well as attracting talented young people to this area and creating opportunities for their professional growth. In 2022, MCMU received 640 million rubles, NOMC – 480 million rubles. About,

Increasing the speed and volume of data transfer is in demand in the field of quantum cryptography, quantum communications and the Internet of things. Researchers from the St. Petersburg International Mathematical Institute named after Leonard Euler have received new theoretical results, which in the future will increase the accuracy of data transmission, or, with a given accuracy, reduce the amount of information. This will increase the speed of its delivery.

Research results of the MCMU “Mathematical Institute named after A.I. V. A. Steklov RAS»will make domestic systems of quantum cryptography more resistant. For this, scientists have developed fundamentally new mathematical methods for estimating the speed of generating a secret key in quantum cryptography. They are able to analyze even the most complex cases under realistic (rather than ideal) hardware assumptions that were previously elusive. The results of the study are of particular relevance today, when quantum cryptography begins to develop as a practical commercial technology. “In the future, the team plans to create a unified mathematical model that would take into account different types of equipment imperfections, as well as evaluate the speed of generating a secret key for this model,” Anton Trushechkin, project manager, commented on the results of the study. leading researcher of the Mathematical Institute. V. A. Steklov RAS.

In 2022, the scientific team of the Mathematical Center in Akademgorodok presented an experimental sample of software for spraying devices for various purposes. The scientists emphasize that software designed for processing shadow images of gas-droplet flow can be used in the analysis of spray systems in energy, medicine and the chemical industry. A request for the development of such software was received by the team from Sigma-Pro, a manufacturer of optical measuring systems in Russia.

The Center was faced with the task of creating a module responsible for the segmentation and calculation of droplet characteristics on shadow images. The development and integration of the first version of the module in the software took a little over a year. “At the moment, the team is working on improving the current solution, as well as developing new modules. The results of the work are of high value from the point of view of the development of modern high-performance methods for image analysis. They can be used to create methods and tools for optical research in the field of fluid and gas mechanics and in engineering applications,” said Rustam Mullyadzhanov, Head of the Laboratory of Applied Digital Technologies of the Mathematical Center in Akademgorodok.
Researchers of the Moscow Center for Fundamental and Applied Mathematicsfigured out how to control the movement of satellites in a group flight. Mathematical calculations will allow spacecraft to achieve the desired configuration in the sky, for example, to line up in a given figure or word. The scientific novelty of the work done is related to the features of the systems under study. “On the one hand, we need to build management in the face of a lack of measurement information and management restrictions. On the other hand, it is necessary to provide the required motion parameters, often in real time, and the features dictated by such systems are taken into account when conducting a study. Classical methods do not give the desired result, so it is necessary to develop new approaches or adapt existing ones,” said Mikhail Ovchinnikov, head of the department and chief researcher at the Institute of Applied Mathematics. M.V.

World-class mathematical centers actively cooperate with scientific and educational mathematical centers (NOMC). Their work is aimed at creating a single environment that unites the system of higher, general and additional education and mathematical science along the entire trajectory of education: school – university – postgraduate studies – the first steps in a scientific career. In 2022, almost 50 thousand schoolchildren, students, undergraduates and graduate students took part in the work of the NOMC network, which organized 253 events. Scientific conferences, seminars, master classes, conventions and congresses are actively held on the basis of the centers: this year they were attended by 3.5 thousand Russian and foreign scientists.

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