On the Sylvester-Gallai Theorem
Date: Wed, Sep 26, 2012
Location: PIMS, University of British Columbia
Conference: PIMS/UBC Distinguished Colloquium
Subject: Mathematics, Algebraic Geometry
Class: Scientific
Abstract:
The Sylvester-Gallai Theorem states that, given any set P of n points in the plane not all on one line, there is at least one line through precisely two points of P. Such a line is called an ordinary line. How many ordinary lines must there be? The Sylvester-Gallai Theorem says that there must be at least one but, in recent joint work with T. Tao, we have shown that there must be at least n/2 if n is even and at least 3n/4 - C if n is odd, provided that n is sufficiently large. These results are sharp
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