Regional branch of V.I. Romanovsky Institute of Mathematics of Uzbekistan Academy of Sciences in Khorezm region was organized according to the paragraph 17 of the Decree of the President of the Republic of Uzbekistan dated May 7, 2020 No DP-4708. In accordance with Annex 2 of this Decree, the department involves 10 research staff and the office of the department is located at the Urgench State University. Currently, DSc. S.A. Imamkulov is head of the department. In the department, Academician A. Sadullaev, DSc. G. Urazboev, leading researcher B.Babajanov, senior researchers Z.Ibragimov, U.Xoitmetov, A.Atamuratov, B.Yusupov, A.Babadjanova and junior researcher Sh. Atanazarova also conduct scientific activities.

The department is currently conducting research in the following areas:

- Non-associative Lie and Leibniz algebras and their local derivation;

- Analytical continuation of functions in multidimensional complex space;

- Complex potentials and its application;

- Theory of analytical functions in parabolic polynomials;

- Direct and inverse spectral problems for differential operators and their applications.

- Local and 2-local derivations and automorphisms on Leibniz algebras;

- Investigation of functions with one-dimensional holomorphic continuity in multidimensional complex space;

- Study of the class of α-separat-subharmonic functions;

- Approximation of analytical functions to simple functions (polynomials) in parabolic polynomials.

- Determined metric charakteristics of removable singularity sets of m-subharmonic and α-subharmonic functions.

-It is proved an analogue of Osgood-Brown theorem for separately harmonic functions.  It is proved several theorems about properties of  removable singular sets of separately harmonic functions

It is proved real analytic version of  Hartogs’s theorem about analytic extension along fixed directions and real analytic version of well-known Forellies theorem.  Here although real analytic function admits real analytic extension along each line, it doesn’t have to be real analytic on domain that is formed by union of all such lines. But even so we can give total description of structure of the set where function is not real analytic.

-Determined conditions of regular parabolicity of complements of  Weierstrass algebroidal sets in complex spaces. Given description of polynomials on this type of manifolds.

--Integrated the Harry Dym equation with an integral type source in the class of the decreasing functions;

- Integrated the periodic Harry Dym equation with a source in the class of the periodic functions

- Integrated the semi-discrete Sine-Gordon equation with a self-consistent source in the class of the decreasing functions

- Integrated the Kortewege-de Vries equation with a loaded source in the class of the decreasing functions

- Integrated the Kortewege-de Vries equation with a loaded source in the class of the decreasing complex valued functions