# Main research areas represented at the department

## 1. Scientific School of Probability Theory, Mathematical Statistics and Theory of Stochastic Processes.

Kyiv Probability School is well known in mathematical world across the globe. Among its founders and prominent researchers are B.V. Gnedenko, I.I. Gikhman, A.V. Skorokhod, V.S. Korolyuk, M.I. Yadrenko – these are figures without whom it is impossible to imagine modern probability theory and theory of stochastic processes. The history of this scientific school is closely related to the development of probability theory at KPI as well as at our department.

Since V.P. Ermakov, who in 1899 became the head of the Department of Higher Mathematics at the KPI, and was, in particular, the author of the coursebook in probability theory, well-known probability specialists have been working at the Institute throughout its history. Thus, in 1930-1938 in KPI there was working academician of All-Ukrainian Academy of Science M.P. Kravchuk, whose scientific results (in particular, Kravchuk matrices and Kravchuk polynomials) are intensively used in many fields of probability theory. For almost half a century (from 1951 to 1997) both scientific and academic interests of academician Yu. L. Daletsky, the author of fundamental works on infinite-dimensional and stochastic analysis, were tightly connected with KPI. In the sequence of famous names one cannot avoid mentioning academician, acknowledged specialist in queuing and reliability theory, first dean of the Faculty of Applied Mathematics, I.M. Kovalenko, who was working at the KPI from 1990 to 1994.

Further development of probability theory at the KPI cannot be imagined without V.V. Buldygin, who occupied the position of the head of Department of Mathematical Analysis and Probability Theory from 1986 to 2012. A world-renowned mathematician, a prominent representative of the Kiev Probabilistic School, author of 7 monographs and about 300 articles, he has made history in mathematics with his fundamental results on sums of random elements in Banach spaces, study of sub-Gaussian and pre-Gaussian random variables and processes, study of various classes of pseudo-regularly varying functions and their applications to various problems of probability theory and theory of stochastic processes. V.V. Buldygin supervised 13 Candidates of Science (including 3 associate professors, who are currently working at the department – O.O. Demyanenko, A.B. Ilienko, M.K. Ilienko) and 3 Doctors of Sciences. In particular, he was a scientific supervisor of his follower – prof. O.I. Klesov, the current head of Department of Mathematical Analysis and Probability Theory. In 2002, V.V. Buldygin was awarded the State Prize of Ukraine for achievements in the field of probability theory and theory of random processes.

Since 2012 O.I. Klesov, academician of the Academy of Higher Education of Ukraine, a highly recognized in mathematical world specialist in probability theory and theory of random processes, is being the head of Department of Mathematical Analysis and Probability Theory. His scientific interests include limit theorems for random fields defined on multi-dimensional lattices, generalized renewal processes, pseudo-regularly varying functions, etc. O.I. Klesov nurtured 4 Candidates of Sciences, who continue their scientific and academic activities at the Department (associate professor O.A. Tymoshenko, lecturers N.V. Kruglova, I.P. Blazhievskaya, V.V. Pavlenkov).

Another striking representative of the probabilistic school at the department is prof. O.V. Ivanov, a world-known specialist in nonlinear regression analysis and statistics of random processes. O.V. Ivanov has scientifically brought up 4 Candidates of Sciences, three of whom are lecturers of the department.

Another bright figure at the department, who represents the modern Probability school, is prof. A.Yu. Pilipenko, an acknowledged specialist in stochastic analysis and stochastic differential equations.

Scientific achievements of the department's Probability School members are recognized worldwide as significant and their works are widely cited by Ukrainian and foreign specialists. Our colleagues are often invited to hold plenary presentations on prestigious international conferences and workshops. Besides, our specialists are constantly involved in joint research projects with colleagues from universities in Germany (Cologne, Ulm and Paderborn), France (Cergy Pontoise), Switzerland (Bern), Norway (Oslo), Austria (Vienna), and publish collaborative works with colleagues from Australia, USA, Canada, Germany, France, Switzerland, Norway, Poland, Hungary, United Kingdom, Spain and other countries.

The department on a regular basis runs a prestigious scientific seminar "Statistical Problems for Random Processes and Fields", which for young specialists, who are about to defend their PhD or doctoral theses, is an unwritten necessary step to pass through. Moreover, due to joint efforts of the department's stuff the electronic scientific journal ''Mathematics in Modern Technical University'' was established.

## 2. Research in Mathematical Analysis

As it is well-known, mathematical analysis is one of the most extensive fields of mathematics and covers many different modern trends. Except colleagues interested in mathematical analysis in its classical sense, our department has assembled several specialists that few can boast, which represent different modern fields of mathematical analysis. Among them are specialists in integral transforms and theory of special functions, functional analysis and its application to the boundary problems of mathematical physics, function theory, harmonic analysis, etc. Our department is proud of its colleagues who have achieved significant results in the sphere of their scientific interests.

A bright representative of the scientific school of Integral Transforms and the Theory of Special Functions at the department is prof. N.O. Virchenko. Academician of the Academy of Sciences of Ukraine, member of the Ukrainian, American, Belgian, Australian, Edinburgh, London Mathematical Societies, she is a well-known specialist in the world in the theory of integral transforms and special functions, as well as their applications to differential and integral equations. N.O. Virchenko is the founder and long-time organizer of the International Scientific Conference in honor of academician M. Kravchuk, which is regularly held at the department and attracts many well-known Ukrainian and foreign participants.

A widely known person who represents the field of functional analysis at the department is prof. V.A. Mikhailets. Among his broad scientific interests are spectral theory of operators and its applications to differential equations of mathematical physics. He is a supervisor to several young specialists at the department.

Ukrainian School of Theory of Functions, founded by V.K. Dzadyk and O.I. Stepanets, is well known in mathematical world. Two prominent representatives of this school work at our department – prof. P.V. Zaderey and prof. V.S. Romanyuk. P.V. Zaderei's scientific interests include theory of functions of real and complex variables, harmonic analysis and approximation theory, while V.S. Romanyuk is mainly interested in approximation theory of functions of one and many variables.

In total 11 highly qualified specialists in Mathematical Analysis (3 Doctors of Sciences and 8 Candidates of Science) form a sustainable basis for academic and research activities at the department.

## 3. Research in Differential Equations.

Studies in the field of Differential Equations are traditional for Kyiv mathematicians. The world-famous is the school of the academician of the NAS of Ukraine A.M. Samoilenko, who continued glorious traditions, laid down by the prominent scientists M.M. Bogolyubov and Yu.O. Mitropolsky. Former PhD students of A.M. Samoilenko, associate professors Z.P. Ordinskaya, K.Yu. Mamsa, G.F. Nefedova are currently working at the department.

## 4. Research in Mechanics of Materials.

A well-known specialist in mechanics of materials, prof. Ya. Rushchitsky, is working at the department since 1987. A Corresponding Member of the NAS of Ukraine, a recognized specialist in mechanics, he is highly respected and valued in the world scientific community. His works are devoted to various issues of applied mechanics. Besides, there are two more specialists at our department, representing this branch of Science, namely, associate professors Ya.V. Simchuk, T.V. Ivanenko.