ECE Seminar Series

Joint Electrical and Computer Engineering Department and Computer Science Department Special Seminar Sponsored by ISTeC

Title: The Algebraic Geometry of Persistence Barcodes
Speaker: Gunnar Carlson
Affiliation: Stanford University
Day: Tuesday, October 21, 2014
Time: 1:00 pm - 2:00 pm
Location: TILT 221

Abstract: Persistent homology associates to a finite metric space an invariant called a persistence barcode, which often allows one to infer the homology of and underlying space from which the finite sample is obtained. These barcodes have numerous applications, and from these applications it is clear that it is very valuable to organize the set of all barcodes in some way. This can be done as a metric space, and we will see that it can be done as an infinite dimensional analogue of an algebraic variety. We will also discuss applications, including applications of the "coordinatization" of the set of barcodes.

Bio: Gunnar Carlsson: B.A. Harvard 1973, Ph.D. Stanford 1976, Ann and Bill Swindells Professor at Stanford University. Has worked in various areas of homotopy theory, equivariant algebraic topology, and algebraic K-theory. Proved "Segal's Burn- side Conjecture" as well a "Sullivan's fixed point conjecture". Sloan research fellow, invited speaker at 1986 ICM. In recent years has been developing topological data analysis, the study of the "shape" of point cloud data. Led a multi-university DARPA initiative on this topic.