|DATE:||Wednesday, January 30th|
|TIME:||16:30 PM - 17:30 PM|
|PLACE:||McConnell 103 (please note room change!)|
|TITLE:||Sylvester's Conjecture in Metric Spaces|
|SPEAKER:||Vasek Chvatal, Department of Computer Science Rutgers, the State University of New Jersey|
Sylvester conjectured in 1893 and Gallai (and others) proved
some forty years later that, for every finite number of points in a
Euclidean space that are not all collinear, there is a line containing
precisely two of these points. With a suitable definition of a line in
a metric space, this conjecture generalizes as follows: in every
finite metric space, there is a line consisting of either all the
points or precisely two points.
I will present first the suitable definition and then meagre evidence in support of the arrogant conjecture. In addition, I will rant a bit about the ternary relation of betweenness in metric spaces.