 n
the interview below, in-cites talks with Professor Andrei
Zelevinsky about his highly cited work in Mathematics.
According to Essential
Science Indicators ,
Professor Zelevinsky’s record in this field includes 24
papers cited a total of 215 times to date. His work recently
garnered the highest percent increase
in total citations in this field. Professor Zelevinsky is a
member of the Department of Mathematics at Northeastern
University in Boston, Massachusetts.
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Why, in your view, is your
work highly cited?
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“My current work grows from the questions that I started to think about a very long time ago.”
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Obviously, I can only offer some guesses here. Here are some
possible reasons: first, I try to address natural questions whose
significance can be understood without going into too many
technicalities. Second, the topics addressed cut across several
mathematical disciplines, and so have a better chance to attract the
attention of a wider mathematical audience. For example, since 1997
when I started posting my papers on the Math Archive, they have
appeared in six different primary categories: Combinatorics, Quantum
Algebra, Algebraic Geometry, Representation Theory, Rings and
Algebras, and High Energy Physics (view).
Third, I try to write as carefully and precisely as I can, pay a lot
of attention to the choice of notation and terminology, try to
explain things in simplest possible terms, and usually spend a lot
of time revising each paper before submitting it for publication.
And finally, it does not hurt that several of my papers are
published in highly selective journals such as Advances in
Mathematics, Journal of the American Mathematical Society,
Inventiones Mathematicae, and Annals of Mathematics.
What are the circumstances which led you to your work?
There are no special circumstances I can think of. My current
work grows from the questions that I started to think about a
very long time ago. In fact, some of the more recent ideas can be
traced back to some work done during my graduate and even
undergraduate years at Moscow State University in the 1970s
(although this connection may be not so obvious).
Would you summarize for us briefly your main
points of interest in your work?
I am not sure how technical you want me to be here. For the last
several years my work has been focused on cluster algebras, a new
class of commutative rings introduced jointly by Sergey Fomin and
myself in the spring of 2000. One of our main motivations for this
new concept was our desire to understand in more concrete and
constructive terms the canonical basis for quantum groups and their
representations introduced by George Lusztig and Masaki Kashiwara in
the beginning of 1990s. I very much like the fact that these
concepts have many connections in different areas of mathematics and
mathematical physics.
How would you describe the significance of this work for
your field?
This is probably not for me to judge, but I guess it is safe to
say that my work offers a fresh approach to some of the natural
problems in the field, and that this approach may be more elementary
and "down-to-earth" than many other existing approaches.
How much has this research advanced since you first started
publishing on it?
A lot! I am particularly happy that my current work has attracted
the attention of several very strong and active mathematicians who
are advancing the subject very rapidly. You can trace the ongoing
progress on cluster algebras using the online portal created and
maintained by Sergey
Fomin.
Where do you see this research
going 10 years from now?
I find this hard to predict, especially since in "pure"
mathematics things are happening on a time scale very different from
other scientific disciplines.
It is not terribly unusual, for example, that mathematicians can
find inspiration for their current research in some work done 200
years ago (this happened to me a few times in my own work). I cannot
think of another field of science where such things are possible. So
there is always a chance that some area of mathematics may become
dormant for a substantial period of time, and then become very
active again. However, returning to my particular area, I feel safe
to say that if the current progress continues at the same rate for
another 10 years, the area will undergo a substantial
transformation, and possibly some of the main open problems will be
solved completely.
Professor Andrei Zelevinsky
Department of Mathematics
Northeastern University
Boston, MA, USA
| Dr. Andrei Zelevinsky's
most-cited paper with 32 cites to date: |
|
Fomin S and Zelevinsky A, "Double Bruhat cells and total positivity,"
J. Amer. Math. Soc. 12(2): 335-80, April 1999. |
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Source:
Essential Science Indicators |
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