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Department of Mathematics and Computer Science (back)
Eastern Illinois University
Announces a CBMS Regional Conference Featuring
Vitaly Bergelson, Ohio State University
Topic: Ergodic Ramsey Theory- A Dynamical Approach to Static Problems
Dates: June 22-28, 2008
The conference is funded by an NSF grant. It will consist of a series of 10 lectures
from June 23-27 which will be collected into a monograph. To see the schedule of talks and to apply for funding see (tentative deadline April 21, 2008)
www.ux1.eiu.edu/~prcoulton/cbms08
The main focus of this conference will involve
the mutually perpetuating interplay between ergodic
theory, combinatorics and Diophantine analysis. Ergodic theory has its
roots in statistical and celestial mechanics. In studying the long term
behavior of dynamical systems, ergodic theory deals with such
phenomena as recurrence and uniform distribution of orbits.
Ramsey theory, a branch of combinatorics, is concerned with the phenomenon
of preservation of highly organized structures under finite partitions.
On the other hand, Diophantine analysis concerns
itself with integer and rational solutions of systems of polynomial equations.
Ergodic Ramsey theory links these three distinct areas of mathematics
together in a beautiful and intricate way. This leads to spectacular
proofs of old conjectures and to the opening of new
promising vistas of research.
Ergodic Ramsey Theory was initiated with
H. Furstenberg's ground breaking paper in
Journal d'Analyse (1977) in which he introduced an
ergodic-theoretic approach to certain classes of problems in additive
number theory and Ramsey theory and obtained a new proof of the celebrated
Szermeredi's theorem on arithmetic progressions. Since that time the
ergodic theory approach has led to strong combinatorial results most of
which do not have conventional combinatorial proofs.
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