| 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.