# On the Sylvester-Gallai Theorem

Speaker:

Ben Green
Date:

Wed, Sep 26, 2012
Location:

PIMS, University of British Columbia
Conference:

PIMS/UBC Distinguished Colloquium 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

Photos of this event are also available.

Photos of this event are also available.