Title: | A Combinatorial Gauss-Bonnet Theorem |

Speaker: | Robert W. Bell Assistant Professor Department of Mathematics and Lyman Briggs School of Science Michigan State University |

Abstract: | The classical Gauss - Bonnet theorem for a closed surface S says thatintegral of the curvature over S depends only on the topological type ofS. For instance, although the unit sphere x^{2} + y^{2} + z^{2} = 1 and theellipsoid 3x^{2} + 5y^{2} + 7z^{2} = 1 are curved differently, if we integratetheir curvatures, we obtain the same value in both cases because thesphere and the ellipsoid are topologically the same surface.We will prove a combinatorial generalization of the Gauss - Bonnet theoremfor two dimensional polyhedra. As a corollary, we will deduce theclassical theorem. No background is required for core of the talk;however, relating the combinatorial theorem to the classical one requiressome acquaintance with vector calculus. |

Location: | Palenske 227 |

Date: | 2/8/2007 |

Time: | 3:10 PM |

@abstract{MCS:Colloquium:RobertWBell

AssistantProfessor

DepartmentofMathematicsand

LymanBriggsSchoolofScience

MichiganStateUniversity:2007:2:8, author = "{Robert W. Bell

Assistant Professor

Department of Mathematics and

Lyman Briggs School of Science

Michigan State University}", title = "{A Combinatorial Gauss-Bonnet Theorem}", address = "{Albion College Mathematics and Computer Science Colloquium}", month = "{8 February}", year = "{2007}" }