# Mathematics Colloquia and Seminars

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### Homology as a tool for shape description and feature recognition

**Geometry/Topology**

Speaker: | Gunnar Carlsson, Stanford University |

Location: | 693 Kerr |

Start time: | Tue, May 6 2003, 4:30PM |

The problem of systematically recognizing two-dimensional objects in 3-space is a difficult one, particularly when one wants to recognize families of objects (i.e. rectangular prisms vs. simplices vs ellipsoids) or objects which have singular behavior. In this talk we will discuss how homological invariants can play a role in performing this kind of recognition. This will require making various constructions on the objects in question, since we frequently deal with objects which are contractible and therefore would be indistinguishable from a single point by naive application of homology. We will also discuss how to obtain topological information when one only has "point cloud data", i.e. finite but large sets of points sampled from the object.

This is part of the BATS conference. There will be a dinner afterwards.