Yuriy Drozd (dedicated to 75th Birthday)
On October 15, 2019 an outstanding Ukrainian mathematician, one of the founders of Kyiv algebraic school Yuriy Drozd celebrated his 75th birthday.
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| Дата: | 2019 |
|---|---|
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2019
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188484 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Yuriy Drozd (dedicated to 75th Birthday) // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. C-F. — англ. |
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irk-123456789-1884842023-03-03T01:27:09Z Yuriy Drozd (dedicated to 75th Birthday) On October 15, 2019 an outstanding Ukrainian mathematician, one of the founders of Kyiv algebraic school Yuriy Drozd celebrated his 75th birthday. 2019 Article Yuriy Drozd (dedicated to 75th Birthday) // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. C-F. — англ. 1726-3255 http://dspace.nbuv.gov.ua/handle/123456789/188484 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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On October 15, 2019 an outstanding Ukrainian mathematician, one of the founders of Kyiv algebraic school Yuriy Drozd celebrated his 75th birthday. |
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Yuriy Drozd (dedicated to 75th Birthday) |
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Yuriy Drozd (dedicated to 75th Birthday) Algebra and Discrete Mathematics |
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Yuriy Drozd (dedicated to 75th Birthday) |
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Yuriy Drozd (dedicated to 75th Birthday) |
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Yuriy Drozd (dedicated to 75th Birthday) |
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Yuriy Drozd (dedicated to 75th Birthday) |
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yuriy drozd (dedicated to 75th birthday) |
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Інститут прикладної математики і механіки НАН України |
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2019 |
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http://dspace.nbuv.gov.ua/handle/123456789/188484 |
| citation_txt |
Yuriy Drozd (dedicated to 75th Birthday) // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 2. — С. C-F. — англ. |
| series |
Algebra and Discrete Mathematics |
| first_indexed |
2025-07-16T10:34:03Z |
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2025-07-16T10:34:03Z |
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1837799356961390592 |
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“adm-n4” — 2020/1/24 — 13:02 — page C — #3
Yuriy Drozd
(dedicated to 75th Birthday)
On October 15, 2019 an outstanding Ukrainian mathematician, one
of the founders of Kyiv algebraic school Yuriy Drozd celebrated his 75th
birthday.
Yuriy Drozd was born in Kyiv, his mother was a physician and father
an engineer. During the Second World War, they both served in the Red
Army as army officers.
Yu. Drozd was interested in mathematics already while studying at
school. In 1961 he became a winner of the 1st Mathematical Competition
of Ukrainian Republic and of the 1st Mathematical Competition of the
Russian Federative Republic. After graduation from high school, Yu. Drozd
became a student of the Faculty of Mathematics and Mechanics of the
Taras Shevchenko Kyiv State University. He graduated from the university
in 1966, main results of his diploma thesis (written under the supervision
of A. Roiter) were published in “Doklady AN SSSR” and influenced
the development of the theory of integral representations. Yu. Drozd
continued his postgraduate education at the Institute of Mathematics
of Ukrainian Academy of Science as a Ph.D. student of I. Shafarevich.
In 1969, Yu. Drozd began his academic carrier in the Kyiv State University,
where he advanced from assistant professor to full professor, being the
“adm-n4” — 2020/1/24 — 13:02 — page D — #4
D Yuriy Drozd
head of the chair of Algebra and Mathematical Logic from 1980 till 1998.
In 1970, Yu. Drozd defended his dissertation “Some questions of the theory
of integral representations” at the Steklov Institute of Mathematics in
Moscow, the leading mathematical institution of the former USSR. This
thesis contained a criterion for a commutative order to have only finitely
many indecomposable lattices, structure results on hereditary and Bass
orders and many other results, which played a central role in the theory
of integral representations afterwards.
In the 1970s, Yu. Drozd began to study matrix problems, a new branch
of algebra and representation theory. His famous “tame-wild theorem”
states that every finite dimensional algebra over an algebraically closed
field has either finite, or tame, or wild representation type. This striking
result sets a milestone of the modern representation theory of finite
dimensional algebras. There were series of international mathematical
conferences entirely devoted to the “tame-wild” questions area. Jointly
with V. Bondarenko, Yu. Drozd described all finite groups that have
tame representation type over a field of positive characteristic. In 1981,
he defended his Dr. Sci. dissertation “Matrix methods in representation
theory and ring theory” at Lenigrad State University.
A great contribution of Yu. Drozd to the development of modern alge-
bra was application of the technique of matrix problems to get exhaustive
classification results in other areas of mathematics, including algebraic
geometry, algebraic topology, commutative algebra, and representation
theory of Lie algebras.
At the beginning of the 1980s, Yu. Drozd initiated a new direction
of research at the Kyiv state university devoted to the study of special
classes of infinite dimensional representations of simple Lie algebras. Using
the technique of matrix problems, he classified bounded representations
of the Lie algebra sl(2) over an arbitrary field of positive characteristic.
Later, jointly with V. Futorny and S. Ovsienko he investigated new classes
of representations of Lie algebras and algebraic groups: weight represen-
tations, Gelfand-Zeitlin representations and others. The obtained results
and developed methods became standard tools for specialists working in
this area of representation theory.
Yu. Drozd made an outstanding contribution to the representation
theoretic study of Cohen-Macaulay modules over curve and surface singu-
larities. Together with A. Roiter, he proved that simple curve singularities
have only finitely many indecomposable Cohen-Macaulay modules. In a se-
ries of joint works with G.-M. Greuel, he proved semi-continuity/finite-
tame-wild-trichotomy of the representation type of reduced curve sin-
“adm-n4” — 2020/1/24 — 13:02 — page E — #5
Dedicated to 75th Birthday E
gularities, explicitly characterizing singularities of tame representation
type. In a subsequent joint work with I. Kashuba and G.-M. Greuel,
Yu. Drozd established tameness of surface cusp singularities. In the last
decade, together with I. Burban, Yu. Drozd discovered a new class of tame
matrix problems called decorated bunches of chains and proved using
them tameness of degenerate cusp surface singularities. Together with
V. Gavran, he established tameness of some non-commutative analogues
of minimally elliptic surface singularities.
This direction of research activity of Yu. Drozd was closely related with
the study of vector bundles and torsion free sheaves on singular curves.
Together with G.-M. Greuel, Yu. Drozd proved tame-wild dichotomy for
the categories of vector bundles and torsion free sheaves on a projective
curve. In a subsequent joint works with I. Burban, the latter results
were generalized for coherent sheaves as well as on the corresponding
derived categories. In a joint work with L. Bodnarchuk and G.-M. Greuel,
Yu. Drozd applied again the technique of matrix problems to classify simple
vector bundles on degenerate elliptic curves of wild representation type.
In the 1990s, Yu. Drozd began a fruitful collaboration with H.-G.Baues
in algebraic topology. In several joint papers, they used the technique
of matrix problems to achieve a crucial progress in stable homotopic
classification of polyhedra.
In 2000s, Yu. Drozd proved semi-continuity of representation type for
the bounded derived category of a finite dimensional algebra. Together
with I. Burban, he established derived tameness of various classes of
finite dimensional algebras. In a joint work with V. Bekkert, Yu. Drozd
proved discrete-tame-wild trichotomy theorem in the framework of derived
categories of finite dimensional algebras.
One of the current directions of the research of Yu. Drozd is devoted
to the non-commutative algebraic geometry. In the 1990s, he introduced
the notion of a nodal order and proved that these are the only orders of
discrete/tame representation type. The global analogues of nodal orders,
the so-called tame non-commutative nodal projective curves, appeared
recently in a quite essential way in the framework of the homological
mirror symmetry for compact surfaces with non-empty boundary.
These and other results of Yu. Drozd were published in top inter-
national journals. He had more than 30 Ph.D. students, four of whom
later defended Dr. Sci. dissertations. From 2006 till now Yu. Drozd is
the head of the Department of Algebra and Topology of the Institute
of Mathematics of National Academy of Science of Ukraine, the main
mathematical organization in Ukraine.
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F Yuriy Drozd
Yu. Drozd wrote several university textbooks, many students use his
“Finite Dimensional Algebras” (with V. Kirichenko), “Galois Theory”,
“Theory of Algebraic Numbers”, “Introduction to Algebraic Geometry”,
“Basic Mathematical Logic”, “Discrete Mathematics” and others. The book
“Finite Dimensional Algebras” was first published in 1980 in Kyiv. In 1983,
it was translated from Russian to Chinese and Spanish. In 1994, an English
translation of this book was published by Springer-Verlag. This book is
one of the most used textbooks about finite-dimensional algebras in the
world.
The book “Introduction to Algebraic Geometry” (based on the lecture
course given by Yu. Drozd at the University of Kaiserslautern in the
winter term 1998/99) is the first and so far the only textbook in algebraic
geometry written in Ukrainian language.
Outstanding research achievements of Yu. Drozd were widely recog-
nized by mathematical community. In 2012, he was elected the corre-
sponding member of the National Academy of Science of Ukraine. In 2007,
Yu. Drozd was awarded the State Prize of Ukraine. In 2017, he was
elected president of Ukrainian Mathematical Society. Yu. Drozd is the
Editor-in-Chief of the journal “Algebra and Discrete Mathematics” and a
member of editorial boards of many mathematical journals, in particular
“European Journal of Mathematics”, “Ukrainian Mathematical Journal”
and others. He is one of the founders of the biannual International Alge-
braic Conference in Ukraine (The first Conference was held in 1997 and
the last-to-date in 2019). He worked in organizing committees of many
international conferences around the world. Yu. Drozd is also one of the
organizers of the Algebra Seminar in Kyiv University, which is one of the
most important modern algebra seminars in Ukraine.
We warmly congratulate Yuriy Anatolijovych Drozd on the occasion
of his 75th birthday and wish him strong health and many successful years
of research and teaching.
V. Bavula, V. Bekkert, O. Bezushchak, V. Bondarenko,
Ie. Bondarenko, I. Burban, V. Futorny, R. Grigorchuk,
L. Kurdachenko, Ya. Lavrenyuk, V. Lyubashenko,
V. Mazorchuk, V. Nekrashevych, A. Oliynyk, B. Oliynyk,
A. Petravchuk, V. Sergeichuk, Ya. Sysak, E. Zelmanov,
A. Zhuchok, Yu. Zhuchok
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