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I. The topics of this book The concept of a matroid has been known
for more than five decades. Whitney (1935) introduced it as a
common generalization of graphs and matrices. In the last two
decades, it has become clear how important the concept is, for the
following reasons: (1) Combinatorics (or discrete mathematics) was
considered by many to be a collection of interesting, sometimes
deep, but mostly unrelated ideas. However, like other branches of
mathematics, combinatorics also encompasses some gen eral tools
that can be learned and then applied, to various problems. Matroid
theory is one of these tools. (2) Within combinatorics, the
relative importance of algorithms has in creased with the spread of
computers. Classical analysis did not even consider problems where
"only" a finite number of cases were to be studied. Now such
problems are not only considered, but their complexity is often
analyzed in con siderable detail. Some questions of this type (for
example, the determination of when the so called "greedy" algorithm
is optimal) cannot even be answered without matroidal tools."
This is the second volume of the procedings of the second European
Congress of Mathematics. Volume I presents the speeches delivered
at the Congress, the list of lectures, and short summaries of the
achievements of the prize winners. Together with volume II it
contains a collection of contributions by the invited lecturers.
Finally, volume II also presents reports on some of the Round Table
discussions. This two-volume set thus gives an overview of the
state of the art in many fields of mathematics and is therefore of
interest to every professional mathematician. Contributors: Vol. I:
N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F.
Bethuel, P. Bjorstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D.
Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T.
Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollar, D.O.
Kramkov, A.N. Shiryaev, C. Lescop, R. Marz. Vol. II: J. Matousek,
D. McDuff, A.S. Merkurjev, V. Milman, St. Muller, T. Nowicki, E.
Olivieri, E. Scoppola, V.P. Platonov, J. Poeschel, L. Polterovich ,
L. Pyber, N. Simanyi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P.
Tignol, A.P. Veselov, E. Zuazua.
This is the second volume of the procedings of the second European
Congress of Mathematics. Volume I presents the speeches delivered
at the Congress, the list of lectures, and short summaries of the
achievements of the prize winners. Together with volume II it
contains a collection of contributions by the invited lecturers.
Finally, volume II also presents reports on some of the Round Table
discussions. This two-volume set thus gives an overview of the
state of the art in many fields of mathematics and is therefore of
interest to every professional mathematician. Contributors: Vol. I:
N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F.
Bethuel, P. BjA, rstad, E. Bolthausen, J. Bricmont, A. Kupiainen,
D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson,
W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. KollAr,
D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. MArz. Vol. II: J.
Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. MA1/4ller, T.
Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. PAschel, L.
Polterovich, L. Pyber, N. SimAnyi, J.P. Solovej, A. Stipsicz, G.
Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua.
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