Ural Federal University: One of the World’s Scientific Schools Established at the University

Solutions of world significance, famous, world famous scientists, founders of entire scientific and technical branches, hundreds of fundamental research works, school and university textbooks and manuals, scientific contacts all over the world – this is the result of the Ural Algebraic School, one of the oldest in UrFU. Having been established in the middle of the last century as one of the leading schools in the world, it then received a powerful impulse of development due to Lev Shevrin, a remarkable scientist and organizer of science.

The Center of World Mathematical Thought

The year 1966 is considered a starting point in the chronicles of the Ural Scientific School of Algebraic Systems Theory and its Applications in Computer Science founded by Lev Shevrin (1935-2021). That year the school was formed on the basis of the scientific seminar “Algebraic Systems” which Shevrin founded and still exists. In 55 years the number of seminars held has long ago exceeded one thousand. Altogether there have been more than 330 speakers (who have made more than 1700 talks in all), including more than 150 speakers from 50 cities of the former USSR and more than 30 speakers from almost two dozen distant foreign countries.

Lev Shevrin is a direct successor of the founders of the Ural Algebraic School – the outstanding mathematicians Pyotr Kontorovich and Sergey Chernikov, a student of Pyotr Kontorovich, in 1968-2001 – his successor as Head of the Department of Algebra and Geometry (since 1995 – the Department of Algebra and Discrete Mathematics).

Both Kontorovich and Chernikov worked at the Ural Industrial Institute (later the Ural Polytechnic Institute) and at Ural State University (now UrFU). Kontorovich was the first Head of the Department of Algebra and Geometry at Ural State University, which he headed from 1946 until his death in 1968, while Chernikov was the first Head of the Department of Mathematical Analysis, was Dean of the Faculty of Physics and Mathematics, and later worked in Perm and Kiev.

It was through the efforts of Pyotr Kontorovich and Sergey Chernikov that the Ural Algebraic School began to develop in the late 1930s, and its historical roots go back to Academician Otto Schmidt – a major organizer of Soviet science, a Hero of the Soviet Union, a mathematician by education and scientific interests, the founder of the Moscow Algebraic School, and from him – to the great Russian mathematician, the founder of the St. Petersburg mathematical school, Paphnuty Chebyshev.

In the mid-1940s, Aleksandr Kurosh, Head of the Department of Higher Algebra at Moscow State University, characterized one of Pyotr Kontorovich’s scientific works as “the largest phenomenon in the world literature on group theory in recent years” (By the way, in 1942-43, the Faculty of Mechanics and Mathematics of Moscow State University was evacuated to Sverdlovsk). By the 1950s, due to the contribution of Kontorovich, Chernikov, and their students to group theory, the priority algebraic “subject” in the 20th century, Sverdlovsk was recognized as one of the centers of mathematical thought worldwide. It was by this time that the emergence of the Ural Algebraic School became an established event. It is worthy of note that the Third All-Union Algebra Conference, which assembled all the Soviet algebraists in 1960, was held at the Ural State University (the first two were held in Moscow). The birth of international contacts between Sverdlovsk mathematicians also dates back to the 1960s.

Valentin Ivanov and Victor Glushkov are among the first graduates of the school and among the doctors of science in their ranks. The former is a future outstanding specialist in the field of mathematical physics, corresponding member of the Academy of Sciences, winner of the Lenin Prize, the latter is the future founder of Soviet cybernetics, academician, Hero of Socialist Labor, winner of the Lenin and State Prizes. In the post-Soviet period, another representative of the Ural Algebraic School, Ivan Eremin, who created his own scientific school of mathematical programming, was awarded the title of academician.

Another student of Pyotr Kontorovich, Professor Albert Starostin, had been working for many years at the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences. The “academic” branch of the Ural Algebraic School is widely known for its achievements in group theory, graph theory, and algebraic combinatorics. The school is currently headed by Starostin’s student, corresponding member of the Russian Academy of Sciences, and Head of the Department of Algebra and Topology at the Institute of Mathematics and Mechanics, Aleksandr Mahnev.

Monographs, symphonies, cartoons

The research of the Ural School of Algebraic Systems Theory and Its Applications to Computer Science founded by Lev Shevrin encompasses a wide range of topics in the modern theory of basic types of algebraic systems (semigroups, groups, rings, lattices) and their classes (manifolds, etc.). In the last two decades the school has paid much attention to aspects of the theory which find applications beyond algebra proper: in graph theory, in such important branches of computer sciences as formal language theory, combinatorics of words, finite automata theory, computation complexity theory, and in discrete optimization, robotics and bioinformatics. The school has achieved the greatest success in studies of lattice properties, in the structural theory of epigroups and finiteness conditions, in the theory of manifolds, in the theory of pseudomultiplications of finite semigroups, and in solving algorithmic problems.

“In each of these areas, the participants of the seminar own the results that meet the world level and, in some cases, determine this level,” Lev Shevrin noted.

The results of Shevrin’s research are reflected in articles and fundamental reviews published in leading Russian and foreign journals (the total number of scientific publications is close to 2000), in monographs in Russian and English, both original and translated. Lev Shevrin and his students and colleagues are the authors of dozens of encyclopedic articles in Russian and foreign manuals and dictionaries, including the Big Soviet Encyclopedia and the “Mathematical Encyclopedia,” which has been translated into English, Spanish, and Chinese and has influenced the mathematical community far beyond the Soviet Union.

Representatives of the school were and are the editors-in-chief and members of editorial boards of major scientific publications and collections of articles published in our country and abroad, participants, speakers, organizers and leaders of more than 300 scientific symposia, conferences and seminars held in most European countries, as well as in Armenia, Australia, Brazil, Canada, India, Israel, China, Japan, USA and other countries.

The school’s international connections extend to Australia, Austria, Belgium, Canada, China, Czech Republic, Finland, France, Germany, Hungary, India, Israel, Italy, Japan, Poland, Portugal, Serbia, Spain, the United Kingdom, and the United States.

Members of the scientific school conduct a large and diverse pedagogical work at the Institute of Natural Sciences and Mathematics and several other institutes of UrFU. They are the authors of more than 100 textbooks and manuals for students and schoolchildren, two programs in mathematics for students in grades 10-11 with advanced study of physics and mathematics and humanities, several “classic” school textbooks in mathematics and computer science and even three science and fiction books that are designed for young readers and are published not only in Russian but also in 20 foreign languages. Based on one of the books, the Sverdlovsk Film Studio produced three animated films.

Since the early 1990s, the school’s activities have been supported by more than 50 Russian and international grants, including two grants from the Russian President to support leading Russian scientific schools, grants from the Russian Ministry of Education and Science, the Hungarian Ministry of Culture and Education, and Russian and international funds to support science.

One of the world’s leading specialists in the theory of semigroups, the author of more than 200 research papers (including three monographs), several textbooks and training courses, Lev Shevrin was awarded the Jose Vasconcelos International Prize for Education, the Ural State University Prize, and the titles of Honorary Professor of the Ural University, Honorary Scientist and Honorary Worker of Higher Professional Education of the Russian Federation, and Academician of the European Academy of Sciences. It is amazing, but Lev Naumovich found time for composing in spite of his tremendous scientific and pedagogical activities: he wrote a symphony in four movements, as well as the anthem of the Ural Federal University.

The Ural Algebraic School Today

At UrFU, Lev Shevrin’s students teach at the Department of Algebra and Fundamental Informatics and conduct research at the Laboratory of Combinatorial Algebra. The current Head of the Department of Algebra and Fundamental Informatics, Mikhail Volkov, is a laureate of the Landau and Volta prizes in the UNESCO “Science for Peace” program, Honorary Worker of Higher Professional Education of Russia, foreign member of the Academy of Sciences and Arts of Finland, and Commander of the “For Services to the Sverdlovsk Region.

“The origins of finite automata theory, in which I specialize, are in the legacy of the famous British mathematician Alan Turing. His discoveries have completely changed our lives, giving rise to programming, creating the conditions for computers, vending machines, cell phones, and other gadgets. The theory of automata is one of the areas in which our university is at the forefront. My students and scientific “grandchildren” have defended about a dozen dissertations on this topic,” says Mikhail Volkov, co-author of the fundamental reference book on the theory of automata.

In the 1980s, representatives of the third generation of the Ural Algebraic School were awarded doctoral degrees. By the beginning of this decade, some members of the fourth generation of Ural algebraists had earned doctoral degrees. At present more than 50 students of the Ural Algebraic School work at UrFU, and their representatives work at universities and academic institutions of Ekaterinburg, as well as at universities of several foreign countries. The fifth generation of the Ural Algebraic School is on its way.

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