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Mathematics Colloquium


Date:  Tuesday, April 03, 2012

Title:  Algebraic Geometry Spring Lectures: Undecidability in number theory and algebraic geometry

Abstract:  Hilbert's Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be. Further study of Hilbert's Tenth Problem leads also to undecidable problems in algebraic geometry.

Speaker:  Bjorn  Poonen
Institution:  MIT


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