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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2005-2006 MATHEMATICS COLLOQUIUM SERIES 03/02/06 Colloquium Dr. Bryce McLeod University of Pittsburgh Oxford University Shapiro's Inequality Abstract:  This is an open problem which is not fully resolved after more than 50 years. I shall trace the history of development and report the most suitable for graduate students.