In Krasnoyarsk, on the basis of the Siberian Federal University, together with the Institute for Computational Modeling KSC SB RAS, a regional Scientific and Educational Mathematical Center (SEMC) of the East Siberia will be created. The main goal of creating such centers is the development of mathematical education and science in the Russian Federation.

In 2020, four scientific and educational mathematical centers will be created in Russia. This decision was made taking into account the proposal of the Coordinating Council of the Ministry of Science and Higher Education of the Russian Federation on the creation and activities of the regional SEMCs.

The centers will be established in Yekaterinburg, Nizhny Novgorod, Krasnoyarsk and Vladivostok. An application from Krasnoyarsk for the creation of the center was prepared by the Siberian Federal University together with the Institute of Computational Modeling SB RAS. The main objectives of the SEMC in Krasnoyarsk will be the development and popularization of mathematical knowledge in the East Siberian region, as well as staff training, including the involvement of schoolchildren and their teachers in the activities of the Center. Particular attention in SEMC will be paid to training specialists and obtaining high-level scientific results.

“Currently, we are facing several major tasks at different levels. In terms of the educational process, there are plans to create new educational modules, train participants in relevant Russian competitions and increase the number of students in the school of physics and mathematics at the Siberian Federal University. In addition, we will also focus on advanced training of school teachers and on improving  the level of mathematical education in the Krasnoyarsk Region as a whole. As far as science is concerned, our work will be aimed at developing international and regional collaborations, in particular with the countries of the Pacific Basin, and, consequently, we expect an increase in the number of scientific publications, ” says August Karlovich Tsikh, Director of SEMC, professor of the Siberian Federal University.

Within the framework of the Scientific and Educational Mathematical Center at the Institute of Computational Modeling KSC SB RAS, world-class results are expected in the following scientific areas:

- The Center will investigate the original formulations of mathematical models for the dynamics of rheologically complicated elastoplastic, granular and porous media in the form of variational inequalities for thermodynamically consistent differential operators which are fundamentally important for the analysis of generalized (weak) solutions with shock waves and discontinuities. Based on these models, universal computational algorithms will be built to solve a wide range of applied engineering problems adapted to the calculation of discontinuities, taking into account different material resistance to tension and compression.

- In the field of fundamental mathematics, a new algebraic approach to the study of the compatibility of differential equations will be developed, which includes finding classes of infinite-dimensional Lie groups admitting a canonical structure, as well as developing and applying the theory of local contact non-group transformations and defining equations. This approach will find applications in constructing new classes of solutions of the equations of hydrodynamics, in the study of the system of equations of heterogeneous acoustics, i.e. in the construction of new classes of solutions with functional arbitrariness. This approach will allow us to perform a group-theoretical analysis of the equations of the semi-empirical model of a swirling turbulent jet and to construct approximate solutions describing the flow in the far turbulent wake behind a moving body.

- The Center will carry out theoretical research, including the construction, analysis and testing of new correct mathematical convection models to describe the dynamics of non-isothermal hybrid liquid systems which are widely used in the space industry, electronics, materials science, heat power engineering, medicine, chemical and food industries. Based on the developed models, thermocapillary convection problems in multilayer liquid systems will be studied under externally applied heat load (local or distributed) and/or in the conditions of diffusion-type phase transition. To solve the problems, an integrated approach will be used, involving the construction of exact solutions, analysis of their stability, development of effective numerical algorithms for solving emerging spectral problems and direct numerical simulation. The results are expected to be used in the development of smart technologies using various self-organizing properties of liquid substances.

- Within the framework of the project, a fund of algorithms, programs and data on the coordinate-time support of spacecraft will be created. Modern methods for obtaining high-precision ephemeris-time information will be used in developing the basic software  as well as alternative approaches will be suggested which may be more effective. An important component of the project is research study: choosing effective numerical methods for integrating the equations of motion of the spacecraft in orbit; developing methods for solving ill-conditioned systems of linear algebraic equations arising in the refinement of orbit parameters.

“We see our main task in carrying out relevant scientific research with the application of the developed mathematical methods in the natural, engineering and human sciences. Young promising students and researchers will be involved in scientific work in these areas. These are graduate and post-graduate students of the basic department of computational and information technologies under the supervision of Vladimir Viktorovich Shaidurov, corresponding member of the Russian Academy of Sciences, and basic department of mathematical modeling and control processes led by professor Viktor Konstantinovich Andreyev. A major role will be given to organizing and conducting scientific events - meetings and conferences, ” says professor Vladimir Mikhailovich Sadovsky, Director of the Institute for Computational Modeling SB RAS, who is responsible for promoting the project.

One of the key directions of the center development is the organization of conferences in various mathematical areas. The first of them will take place in July of this year. This is the VII All-Russian Conference "Problems with Free Borders: Theory, Experiment and Applications" with the participation of foreign scientists. The conference will be organized by the Institute of Computational Modeling SB RAS and Institute of Mathematics and Fundamental Informatics of the Siberian Federal University; the co-organizers are the Lavrentyev Institute of Hydrodynamics SB RAS and  Kutateladze Institute of Heat Physics SB RAS from Novosibirsk.