Geometry -- from algebraic to arithmetic to absolute

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THE UNIVERSITIES OF SYDNEY AND NEW SOUTH WALES

SCHOOLS OF MATHEMATICS AND STATISTICS

______________JOINT COLLOQUIUM__________________

Speaker: James Borger (ANU)

Date: Friday, 20 May 2011

Time: 14:30

Venue: Room 175 Carslaw Building, University of Sydney

Title: Geometry -- from algebraic to arithmetic to absolute

Abstract:

Classical algebraic geometry is about studying solutions to systems of polynomial equations with complex coefficients. In arithmetic algebraic geometry, one digs deeper and studies the arithmetic properties of the solutions when the coefficients are rational, or even integral. From the usual point of view, it's impossible to go deeper than this for the simple reason that no smaller rings are available -- the integers have no proper subrings. In this talk, I'll explain how an emerging subject, lambda-algebraic geometry, allows one to do just this and why one might care. I will not assume any familiarity with algebraic geometry.