
This
is a special issue of the journal devoted to the jubilee of the
outstanding Ukrainian mathematician, one of the founder of our
journal Professor Yuriy Drozd.
Yuriy Drozd was born on the 15th of October, 1944 in Kyiv,
in a family of officers, participants of the II World War (his
mother was a doctor, his father was an engineer). He was delighted
in mathematics still at school, due to his teacher, Asia Aronivna
Horon. By the way, three of her former pupils became Doctors of
Sciences (the highest scientific degree in the former Soviet Union);
it is interesting that all three of them were working in algebra:
M.Kargapolov, A.Roiter and Y.Drozd. In 1961 Yuriy got the first
prize at the 1st Ukrainian mathematical competition, and at the
first AllRussian mathematical competition. The same year he entered
Kyiv Taras Shevchenko University, Department of Mechanics and
Mathematics. In 1966 he graduated from the University with honours.
His advisor at the University was A.Roiter. Collaboration with
A.Roiter and V.Kirichenko was a valuable experience of the scientific
research for the young mathematician. The main result of his Diploma
work (Master Thesis) was a criterion of finiteness of the set
of indecomposable representations for cubic rings. It was published
in "Proceedings of the Academy of Sciences of the USSR"
and was important for the future development of the theory of
integral representations of rings.
In 1966 Yuriy Drozd entered a graduate study program at the
Institute of Mathematics of the Academy of Sciences of Ukraine.
His advisor there was one of the most prominent Soviet mathematicians
Igor Shafarevich. In February 1969 Yuriy accomplished his graduate
study and since then he was working at the Kyiv Taras Shevchenko
University, Department of Mechanics and Mathematics, Division
of Algebra and Mathematical Logic. There he followed a long track,
form an assistant till a full professor and Head of the Division
(19801998). In 1970 he presented his Candidate (Ph.D.) Thesis
"On Several Questions of the Theory of Integral Representations"
at the Steklov Mathematical Institute in Moscow. The results of
this thesis, such as a criterion of finiteness of the set of indecomposable
representations for commutative orders, structure theory of hereditary
and Bassian orders, new results on the structure of genera, took
since then a central place in the whole theory of integral representations.
In the following years the scientific interests of Yuriy
Drozd broadened. He started his works on a new area, the theory
of the so called "matrix problems." Soon he proved one
of the main results here, the "tamewild dichotomy,"
i.e. the theorem that every finite dimensional algebra is either
representation tame or representation wild. This result was the
origin of a series of works of specialists through the world.
Several conferences were specially devoted to this "tamewild
subject." Yuriy Drozd also implemented the matrix techniques
into new areas, such as the multiplicative theory of ideals and
others. In 1981 he presented to the Leningrad University his Doctor
of Sciences Thesis "Matrix Methods in the Theory of Representations
and Rings".
In eighties Yuriy Drozd initiated at the Kyiv University
investigations of representations of Lie algebras and groups.
In his first paper in this field "On representations of the
Lie Algebra sl(2)" he applied matrix methods to study of
these representations. Further, in collaboration with S.Ovsienko
and V.Futorny, he studied new classes of representations, such
as weight representations, GelfandZetlin representations, representations
of general position of "mixed" linear groups, etc. Now
the achievements of Kyiv mathematicians in these topics are well
known and highly appreciated.
The downfall of the USSR and of the Iron Curtain opened a
new stage in the scientific biography of Yuriy Drozd. In 1989
he was able for the first time to participate in a scientific
conference in the West (it was a meeting of the London Mathematical
Society), though he had got invitations to such conferences regularly
during more than 15 years before. Further on such visits became
usual. From 1992 he was a member of the Scientific Committee of
the International Conferences on Representations of Algebras (ICRA),
which take place every two years. In 1997 he organized an International
Conference on Representation Theory and Computer Algebra in Kyiv.
From 1990 Yuriy Drozd started his fruitful collaboration
with his German colleague G.M.Greuel on investigation of CohenMacaulay
modules. In about two or three years they completely described
representation types of onedimensional CohenMacaulay rings.
For Yuriy it was, in a since, a return to his youth, since this
topic is a variant of the theory of integral representations of
rings. Further they solved the analogous question for vector bundles
over projective curves and for a wide class of twodimensional
CohenMacaulay rings. Since 1998 Yuriy Drozd started collaboration
with another German mathematician, H.J.Baues, in algebraic topology,
which was a completely new area for him. Applying the matrix techniques,
they advanced well in classification of stable homotopy types
of polyhedra.
These topics led Yuriy Drozd to the theory of derived categories.
With his disciples V.Bekkert and I.Burban he extend to these categories
the tamewild dichotomy and gave a complete classification of
complexes in derived categories of a wide class of rings as well
as for tame projective curves.
Now he is successfully continuing these investigations. They
were published in more than 90 papers and served as a basis for
25 Candidate (Ph.D.) Theses of his students (three of them are
now Doctors of Sciences). Yuriy Drozd is the author of several
University textbooks. Especially the book "Finite Dimensional
Algebras" by him and V.Kirichenko was translated by SpringerVerlag
into English and is now the most used by students through the
world. Yuriy Drozd was a visiting professor at the Universities
of Strasbourg, Kaiserslautern, Torun, Santa Barbara, Uppsala.
He gave survey talks as invited lector at the international conferences
and seminars in Japan, Germany, Great Britain, USA, Canada, France,
Mexico, Spain, Brazil. 