|4:00 pm Wednesday, August 24, 2011|
Geometry-Analysis Seminar: Generalizing Furstenberg-Weiss’s topological reformulation of the multidimensional van der Waerden theorem. The (Q,+) case.
by Andreas Koutsogiannis (University of Athens, Greece.) in HB 227
Abstract: Van der Waerden's theorem (1927), a (perhaps the most) fundamental result in Ramsey theory, states that for any finite partition of the set of natural numbers there exists a cell of the partition which contains arbitrary long arithmetic progressions. We present the topological reformulation of the multidimensional van der Waerden theorem which follows from a classical result due to Furstenberg and Weiss (1978). We introduce the notion of a rational dynamical system extending the classical notion of a topological dynamical system and we prove (multiple) recurrence results for such systems via a partition theorem for the rational numbers (A.K-V. Farmaki, 2010), generalizing the previous results. Also, we give some applications of these topological recurrence results to topology, to combinatorics, to diophantine approximations and to number theory. Host Department: Rice University-Mathematics
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