Questions about rational points on curves — the interplay of arithmetic and algebraic geometry — have fascinated mathematicians from Diophantus to the present. Prof. Mazur will mention a few different current ways of proving a fundamental theorem in the subject, and how curious it is that we have such disparate avenues of approach. He will also talk about conjectures, and an application to mathematical logic.

Some prerequisite knowledge on groups and fields will be useful, but the talk should be interesting even without understanding all the technical details. No knowledge of algebraic geometry is required.

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