Seminars/Colloquia/Invited Talks

Seminars

Francis Lazarus

Introduction to Computational Topology

PLACE:	Clark 314
EVENT:	CIS Seminar Series
DATE:	May 3, 2005
TIME:	1:00 - 2:00

Presentation Slides

Abstract

Computational topology deals with effective computations of topological invariants over combinatorial structures. A topological invariant of a (combinatorial) object is left fixed by a transformation that do not alter its topology. A typical transformation is a subdivision of a triangulation. Classical invariants are algebraic, ranging from numbers (number of connected components, Euler characteristic,...) to groups (the fundamental group or the homology groups). When an invariant has multiple representations, such as a set of generators for a group, its computation can be coupled with an optimization problem such as: find the minimal basis for the cycle space of a graph with respect to some length definition. Computational topology arises in many applications including molecular analysis in bioinformatics, computer graphics (morphing, texture mapping), shape and pattern recognition, etc... In this talk I will introduce the main concepts of Computational topology, the fundamental group and the homology groups, and present a state of the art for low dimensional objects, including optimization problems for homotopy of curves on a graph or on a surface.

Brief biography

Francis Lazarus is a research scientist at CNRS (Centre National de la Recherche Scientifique) in Poitiers, France. His current research focus on computational aspects of topology, and more specifically on optimization of curves on surfaces. His research interests also include Computational Geometry and geometric problems in Computer Graphics. He received his doctorate in 1995 from the Department of Computer Science of the University of Paris VII with a thesis on morphing algorithms. He then spent 18 months as a Post-Doc in the IBM T.J. Watson Research Center working on 3D geometry compression and progressive transmission of polygonal models.