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.
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