| 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 x2 + y2 + z2 = 1 and theellipsoid 3x2 + 5y2 + 7z2 = 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}"
}