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Ronald Graham 
2009-07-03 
09:30 - 10:30 
101 , Mathematics Research Center Building (ori. New Math. Bldg.)

A major branch of modern combinatorics, usually called Ramsey theory, studies properties of structures which are preserved under partitions. Its guiding philosophy can be neatly summarized by the statement, "Complete disorder is impossible". In this talk I will survey what is known and what is still unknown from this perspective for solution sets of linear equations over the integers.