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CRM - University of Ottawa Distinguished Lecture Series

TITLE:Algebraic Topology as a Tool for the Analysis of High-Dimensional Data
SPEAKER:Gunnar Carlsson (Stanford University)
DATE:Vendredi, 10 Février 2006
TIME:3:30 pm
ROOM:FTX 147A
ABSTRACT:

Mathematicians have long understood that algebraic topology is a very effective tool for the qualitative description of geometric objects, such as manifolds, simplicial complexes, etc. In recent years, methods and software have been developed which allow one to infer topological invariants for geometric objects given only a finite but large set of points sampled from the objects, perhaps with noise. This now makes it possible to obtain qualitative information about many kinds of high=dimensional data. In this talk, I hope to achieve the following

(1) Argue that qualitative information about data is an important, in some cases the most important aspect of the analysis of the data.
(2) Present the methodology which makes it possible to obtain qualitative information
(3) Illustrate the methods with examples.
(4) Present a conceptual framework describing our ideas.

About the speaker: Gunnar Carlsson received his PhD in algebraic homotopy theory and K-theory from Stanford University in 1976. He was named an Alfred P. Sloan Fellow for the period 1983-1987 and was Professor of Mathematics at Princeton University from 1986 to 1991. His recent hounours include a research grant from the Defence Advanced Research Projects Agency (DARPA) for the project entitled "Topological methods for the analysis of high dimensional data sets and 3D object recognition", which he was awarded for the period 2005-2009 together with collaborators from Stanford University, Duke University, Rice University, and the University of Minnesota. Gunnar Carlsson is editor of several journals, including " K-Theory", "Geometry and Topology", and "Homology, Homotopy, and Applications". Since 1991, he has been a professor in the Department of Mathematics at Stanford University.

Gunnar Carlsson's research lies primarily in algebraic K-theory and homotopy theory. Recently, he has made important contributions to applications of algebraic topology to object recognition theory.