Albion College Mathematics and Computer Science Colloquium

 Title: A Combinatorial Gauss-Bonnet Theorem Speaker: Robert W. BellAssistant ProfessorDepartment of Mathematics andLyman Briggs School of ScienceMichigan 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:RobertWBellAssistantProfessorDepartmentofMathematicsandLymanBriggsSchoolofScienceMichiganStateUniversity:2007:2:8,
author  = "{Robert W. BellAssistant ProfessorDepartment of Mathematics andLyman Briggs School of ScienceMichigan State University}",
title   = "{A Combinatorial Gauss-Bonnet Theorem}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month   = "{8 February}",
year    = "{2007}"
}