### Scientific activity

**Scientific activity****:**

**Algebra va funksional anliz**

Operator algebras, Jordan and Lie structures on von Neumann algebras, Non commutative integration theory and Quantum Probability, Jordan algebras of self-adjoint operators and Jordan Banach algebras, Theory of ordered involutive and Jordan algebras.

Structure of derivations on Operator algebras. Derivations and automorphisms on algebras of unbounded operators on Hilbert spaces, applications in Quantum dynamics. Structure theory non associative algebras, Lie (super)algebras, Leibniz (super)algebras, n-Leibniz algebras, structure theory of algebras, p-adic analysis, evolution algebras and their applications, algebraic geometry.

Dynamical systems, trajectory theory of dinamical systems, nonlinear operators and processes, random walks in random environment, *p*-adic analysis, the Gibbs measures, lattice models of statistical mechanics.quadratic stochastic operators, simplex, trajectory, Volterra and non-Volterra stochastic operators.

**Dinamik sistemalar nazariyasi bo'limi**

Scientific research fields:

Department of the Theory of Dynamical Systems leads in the scientific fields: dynamical systems, differential equations, game theory, optimal control theory, mathematical modeling of chemical and cyclic processes.

**Ehtimollar nazariyasi**

Classical and non-classical variants of the central limit theorem for random sums, Limit theorems satisfying some dependent conditions and taking value in the functional spaces, asymptotic properties of statistic estimates of the constructed information of dependent functional of unknown parameters, functional limit theorems for branching random processes with dependent immigration components, applying the method Monte Carlo to the theory of decision.

__Medical and Biological Informatics__

Applications of artificial intelligence methods in drug development, medicine.

**Дифференциальные уравнения**

Harmonic analysis, spectral theory of differential and pseudo-differential operators, fractional order operators, classical, confluent, generalized hypergeometric functions, pFq Appel, Gorn and Laurichella functions, fundamental solutions, degenerating elliptic, parabolic and hyperbolic equations, direct and inverse problems for fractional order differential equations, boundary value problems for the second and higher order mixed type equations, inverse problems for non-classical equations of mathematical physics, boundary value problems for evolution equations.