Think Locally, Act Globally

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• Prof Kevin Buzzard (Imperial College
• Monday 07 November 2011, 08:30-09:30
• Winstanley Lecture Theatre, Trinity College.

If you have a question about this talk, please contact Mary Fortune.

Are there any rational solutions to x²+y²=-1? No, because there are no real solutions. How about x²+y²=3? Again the answer is no, but one way of showing this is by constructing a ‘local field’ — the 3-adic numbers — which contains the rationals as a dense subfield, and in which it’s easy to check that there are no solutions. It is far easier to solve equations in these local fields than in global fields such as the rationals, and conversely, sometimes solutions in all local fields can imply solutions in a global field too.

This talk is part of the Trinity Mathematical Society series.

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• Guy Emerson's list
• Trinity Mathematical Society
• Winstanley Lecture Theatre, Trinity College
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