Nov 03:  The Sylvester-Chvatal Theorem
                     Xiaomin Chen, Rutgers Univ.

The Sylvester-Gallai theorem asserts that every finite
set $S$ of points in two-dimensional Euclidean space includes two
points, $a$ and $b$, such that either there is no other point in $S$
is on the line $ab$, or the line $ab$ contains all the points in $S$.
V. Chv\'{a}tal extended the notion of lines to arbitrary
metric spaces and made a conjecture that generalizes the
Sylvester-Gallai theorem.  In the talk, we prove this conjecture to be true.

--------------------------------------------------------------------------