## PIMS/UBC Distinguished Colloquium: Ben Green (Cambridge)

- Date: 09/26/2012

Ben Green, Cambridge

Ben Green is the Herchel Smith Professor of Pure Mathematics at the University of Cambridge and a Fellow of Trinity College who has published several important results in both combinatorics and number theory. These include improving the estimate by Jean Bourgain of the size of arithmetic progressions in sumsets, as well as a proof of the Cameronâ€“ErdĂ¶s conjecture on sum-free sets of natural numbers. He is a Fellow of the Royal Society, and has received many prestigious awards including the Salem Prize.

University of British Columbia

On the Sylvester-Gallai Theorem

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.

The talk will give an overview of this problem and the work towards its solution.

Lecture begins at 3:00 pm in ESB 2012, preceded by a reception in ESB 4133 at 2:30 pm