# Events

### Friday, Jan 20, 2017 - 3:00pm - Allen 411

ACT seminar

Some easy to state open problems related to R-trees

Dr. Paul Fabel, Mathematics, Msstate

**Title:** Some easy to state open problems related to *R*-trees

**Abstract:**
"All trains lead to Paris" is the abstract of Evelyn Lamb's recent article in Roots of Unity, her math blog for Scientific American. The idea is that to get from anywhere to anywhere in France, traveling by train you will likely go to Paris, even if (as the crow flies) there's a much shorter route.

The content of the article is a mathematical version of this idea, in which (thinking of the origin (0, 0) as Paris) the distance between planar points (*x*, *y*) and (*z*, *w*) is no longer the usual one, but rather the following. If (*x*, *y*) and (*z*, *w*) and (0, 0) are not collinear, instead of the usual distance we use sqrt(*x*^{2}+*y*^{2}) + sqrt(*z*^{2}+*w*^{2}).

The resulting metric space is an example of an *R*-tree, a metric space so that there is a unique arc between any two points, and moreover the arc length is the distance between the endpoints.

We will discuss some fundamental open questions related to *R*-trees.