# Mathematics Colloquia and Seminars

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### Folds, Intersections, and Inflections for Smooth and Polyhedral Surfaces: Distinguishing Cylinders from Moebius Bands

**Geometry/Topology**

Speaker: | Thomas Banchoff, Brown University |

Location: | 2112 MSB |

Start time: | Mon, Apr 22 2013, 4:10PM |

Any simple closed curve on a surface has a strip neighborhood which is either a cylinder or a Möbius band, and when the surface is situated in Euclidean three-space, there are different geometric ways of distinguishing the two cases. Three related involve counting the number of times the curve intersects the fold curve of the projection of a surface to a plane, or the self-intersection curves of the surface, or the "inflection curves", all of these notions to be defined in the talk. These examples give an introduction to the extrinsic geometry of characteristic classes. The presentation will feature computer graphics illustrations of surfaces in three- and four-space.

There will be a dinner after the seminar