In 55 years, RUDN University has given the world many famous names and important scientific discoveries. For over 15 years, the University has been in the top 10 best universities in Russia for research and innovation.

RUDN University is a recognized large scientific center, a generator of new ideas and developments.

In 2016 the University held a competition of projects with significant achievements in the priority research areas. Each winning project received funding amounting to 10 million rubles for the implementation of its development.

Construction of spherically symmetric stationary solutions of the Vlasov-Poisson system of equations describing the stationary distribution of particles in a gravitational field. Obtaining sufficient conditions for confining high-temperature plasma in a “mirror-trap” fusion reactor.

In the problem of describing the asymptotic properties of generalized solutions of quasilinear parabolic equations in a neighborhood of the time of the singular exacerbation of the boundary regime (i.e. boundary data), at the present time, it were found limiting restrictions on the intensity of the exacerbation leading to solutions with a non zero but finite measure of the blow- up, i.e. the so-called S-modes are described.

Development and research of blood clotting models and description of thrombin production in normal and pathological (hemophilia) cases; comparison with experimental data.

The main goal of the project is to create a noncommutative elliptic theory for a new class of operators associated with the representation of a group by quantized canonical transformations on different varieties.

The project analyzes boundary value problems for elliptic functional-differential equations in bounded domains and half-space, as well as elliptic functional-differential equations in the entire space R^n.

The Project’s objective is to enhance models of optical and quantum-physical devices based on
the wave optical and quantum mechanical effect (QM effect).

Establish a world-class Research Center for solving theoretical problems in probability theory and mathematical statistics, including the application of developed mathematical models to analyze telecommunications networks and systems

Set up a world-class Research Center for solving practical problems in 5G wireless networks in regard to the network technologies and conducting experimental studies

The project is devoted to the development of new qualitative and geometric methods for the study of boundary value problems for differential and functional differential equations, their application to the Vlasov equations (kinetics of high-temperature plasma), the Kato problem of the square root of the operator, mathematical biology and mathematical medicine.