Research Groups

Center's educational seminars

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Digitalization of Mathematical Models and Intelligent Systems for Data Analysis

Research Group Leader: Nikolay Bazhenov, PhD (nickbazh@yandex.ru)            

The project focuses on digitalization of mathematical models based on computational models of bounded complexity, in particular polynomial and automaton computations. Research areas include existence problems for decidable models and computable models, effective enumeration theory, and machine learning.           

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Differential Equations and Dynamical Systems

Research Group Leaders: Gennadii Demidenko, Professor (demidenk@math.nsc.ru), Lina Bondar, PhD                

This group is engaged in researching the solvability problem for forward and inverse problems for non-classical partial differential equations, differential operator equations, integral and integro-differential equations. We also study asymptotic properties of solutions for difference-differential equations.  



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Multivariate Complexity Analysis and Provably Optimal Algorithms

Research Group Leader: Rene van Bevern, PhD (rvb@rvb.su)

This group focuses on the development of parameterized algorithms of NP-hard discrete optimization problems. 

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Algebraic Combinatorics and Combinatorial Algebra: Theory and Algorithms

Research Group Leaders: Andrey Vasil'ev (vasand@math.nsc.ru), Professor, Elena Konstantinova, Professor 

This group is engaged in research and development in several areas of group theory that are closely connected to algorithmic problems. This includes group theory as well as related areas such as algebraic combinatorics, and computational complexity theory.      



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Optimal Control Theory

Research Group Leaders: Sergei Vodopyanov, Professor, Maria Karmanova, Professor (maryka@math.nsc.ru)

This group aims to achieve fundamental results in the following areas of geometric analysis: geometry, geometric control theory and Sub-Riemannian geometry, hypoelliptic equations, quasiconformal analysis, Sobolev spaces theory, and geometric operator theory.

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Geometric Aspects of Mathematical Physics

Research Group Leaders: Iskander Taimanov, Academician of RAS, Andrei Mironov, Corresponding member of RAS (mironov@math.nsc.ru)

This group conducts research on mathematical billiards, commuting differential and difference operators, geodesic streams and related problems of mathematical physics, dynamic systems theory, and differential geometry.  


                          
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Current Trends in Probability Theory and its Applications

Research Group Leaders: Sergei Foss, Professor, Evgenii Prokopenko, PhD (evgenii.prokopenko@gmail.com)          


This group focuses on urn model theory and its application to computer networks theory, random graphs theory, and problems of mathematical linguistics. It is also engaged in developing the theories of decentralized data transfer algorithms and regression analysis with random regressors.

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Algebraic and Logical Methods for Cryptography Problems, Universal Algebraic Geometry and Machine Learning

Research Group Leaders: Vitalii Roman'kov, Professor, Vladimir Remeslennikov, Professor, Alexander Treyer, PhD (treyer@ofim.oscsbras.ru)

This group’s research objectives focus on three related subjects: algebraic cryptography, development of model theoretic approach to machine learning, and algebraic geometry for finite combinatorics. 



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Cryptography and Information Security

Research Group Leader: Natalia Tokareva, PhD (tokareva@math.nsc.ru)

This group is engaged in multiple areas of research including cryptography, discrete math, cryptographic boolean functions (bent functions, APN-functions, etc.,), block ciphers and S-boxes, cryptanalysis of symmetric ciphers, lightweight cryptography and internet of things, blockchain technologies and their applications, quantum and post quantum cryptography. 

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Inverse Problems in Natural Science

Research group leader: Maksim Shishlenin, Professor (mshishlenin@ngs.ru)

This group’s objectives are: the development and numerical realization of a two-dimensional mathematical model of acoustic tomography presented in terms of conservation laws; the study of mathematical statements of models of social, epidemiological, and economic processes; geometric and topological methods in mathematical modeling of porous media; geometric methods in the theory of inverse problems.