# Dartmouth Mathematics Colloquium

#### Thursday, April 17, 1997

**4:00-5:00 pm**

#### 102 Bradley Hall

## Professor Dan Archdeacon

#### University of Vermont

speaks on

### Sewing Ribbons on Graphs in Space

**Abstract.** A ribbon is a rectangle with one side distinguished as the
seam. Suppose that you want to sew the seam of a ribbon onto a graph
embedded in 3-space. Even harder, suppose that you want to
simultaneously sew several ribbons on the same graph. If the seams
intersect in a complicated way, it can be impossible to sew the ribbons in
the desired manner.
In this talk we examine when these sewn ribbon complexes embed in

3-space. We give several characterizations of these spatial ribbons

complexes. We also consider the theoretical and algorithmic

implications of our characterizations. The problem seems to lie right

on the boundary (assuming there is one) between polynomial and

NP-complete problems.

Tea. High tea will be served at 3:30 pm in the Lounge.

**Emmy's. **Certain refreshments will be available at Emmy's after the talk.

**Host. **Michael Orrison is the host. Anybody who is interested in having
dinner with the speaker should contact Michael at 643-2374.