Research Activities and Priority Areas

The Department of Mathematical Analysis currently focuses on research in complex potential theory, m-subharmonic functions, parabolic manifolds, and analytic function theory. Under the supervision of Academician A.S. Sadullaev, a scientific school on the Theory of Functions of Several Complex Variables was established. Young specialists have achieved notable results in these areas.

The department’s main research areas include:

1. ⇒ Theory of m-Potentials and its Applications
   (Scientific supervisor: Prof. B.I. Abdullaev; Researchers: R.A. Sharipov, M. Vaisova, D. Qalandarova, U. Sobirov, J. Ashirov, Q. Akhmedov)
   This direction studies the class of m-subharmonic functions, their measures, m-convex functions, their properties, and applications in physical processes.

2. ⇒ Theory of Analytic Functions on Parabolic Manifolds
   (Scientific supervisor: Prof. A.A. Atamuratov; Researchers: Kh.Q. Kamolov, S. Bekmetova, S. Bekchanov, I. Turakhanov)
   This area investigates the properties of analytic functions on parabolic-type manifolds and their theoretical foundations.

3. ⇒ Integral Formulas in Classical Domains and their Applications
   (Scientific supervisor: Prof. G. Khudayberganov; Researchers: J.Sh. Abdullaev, Z. Matyaqubov, Q. Erkinboyev, S. Khayitboyev, K. Qurbonov)
   Research in this field focuses on classical integral formulas and their practical uses.

      The department’s academic staff has published numerous scientific papers, textbooks, and teaching manuals in both national and international journals. Faculty members also actively participate in international conferences, seminars, and research grant projects.

Research projects carried out jointly with the department

• - From 2012 to 2016, fundamental project No. Ф4-ФA-016928 was completed jointly with the Khorezm Mamun Academy on the topic "Plurigregularity Properties in the Theory of Complex Potentials and Adapted Initial Finite Differential Equations" (supervised by Prof. A. Sadullaev);
• - From 2016 to 2017, fundamental project No. Ф-4-13 was completed on the topic "α-Subharmonic Functions and Potentials" (supervised by M. Vaisova);
• - From 2017 to 2020, fundamental project No. ФA-Ф-4-002 was completed on the topic "M-Subharmonic Functions and Their Applications to Calibrated Geometry" (supervised by Prof. B. Abdullaev);
• - In 2020–2022, the Department of Mathematical Analysis at the Mirzo Ulugbek National University of Uzbekistan will jointly implement the international fundamental project UT-OT-2020-1, "The Monge-Ampère Equation and Extremal Plurisubharmonic Functions" (Project Supervisor: Prof. A. Sadullaev).
• - Currently, the Department of Mathematical Analysis at the Mirzo Ulugbek National University of Uzbekistan and the Department of Mathematical Analysis and Differential Equations at Siberian Federal University, scheduled for 2023–2027, are jointly implementing the international fundamental project IL-5421101746, under the supervision of Prof. B. Abdullaev, on the topic of "Theory of Pluripotentials and Application of Integral Formulas in Problems of Analytic Continuation."

Scientific conferences organized jointly with the department

• - The First USA-Uzbekistan conference on Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton
• - The Second USA-Uzbekistan conference on Analysis and Mathematical Physics, august 8-12, 2017, Urgench State University, Urgench 

Scientific Seminars

     The department, together with the Khorezm branch of the V.I. Romanovsky Institute of Mathematics, is organizing a scientific seminar on "Theory of Complex Potentials and Its Applications." The seminar is held every Friday at 3:30 PM in Room 222 of the Faculty of Physics and Mathematics (seminar leaders Professor B. Abdullaev and Professor A. Atamuratov).

Announcements

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  1) Seminar, September 5, 2025, 3:30 PM. (222 - seminar room​ and online on Zoom)
• Speaker: Sardor Bozorboev, PhD student at the National University of Uzbekistan
• Topic: "Measures of large entropy for polynomial-like maps in several complex variables"
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  2) Seminar, September 12, 2025, 3:30 PM. (222 - seminar room​ and online on Zoom)
• Speaker: Islambek Ismailov, teacher, Department of Mathematical Analysis
• Topic: "Self-affine Domains on the Plane"
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  3) Seminar, September 19, 2025, 3:30 PM. (222 - seminar room​)
• Speaker: Erkinboev Qutlimurot Sanat oglu teacher, Department of Mathematical Analysis
• Topic: "On Matrix Spherical Automorphisms"
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  4) Seminar, September 26, 2025, 3:30 PM. (222 - seminar room​)
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  5) Seminar, October 3, 2025, 3:30 PM. (222 - seminar room​)
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  6) Seminar, October 10, 2025, 3:30 PM. (222 - seminar room​)
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  7) Seminar, October 17, 2025, 3:30 PM. (222 - seminar room​)
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  8) Seminar, October 24, 2025, 3:30 PM. (222 - seminar room​ and online on Zoom)
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  9) Seminar, October 31, 2025, 3:30 PM. (222 - seminar room​ and online on Zoom)
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  10) Seminar, November 7, 2025, at 3:30 PM. (222 - seminar room​ and online on Zoom)
• Speaker: Kobiljon Kuldoshev, teacher, Department of Mathematical Analysis, National University of Uzbekistan
• Topic: "Weighted m-subharmonic measures"
• Annotation: In this talk, we study weighted m-subharmonic measures within the class of m-subharmonic functions. We investigate their fundamental properties and establish several theorems on (m,\psi)-regularity. In particular, we prove that if the weighted (m,\psi)--subharmonic measure is Hölder continuous with respect to a compact set, then it is also Hölder continuous in D. This result is new even in the unweighted case. Furthermore, we introduce the concepts of (m,\psi)--capacity and weighted P_(m,\psi)--capacity, and establish their basic properties.
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