Departmental Colloquium
Gunnar Carlsson
Dept of Mathematics, Stanford University

 

Tuesday, October 21, 2014

Time: 1:00 - 2:00
Location: 221 TILT
Reception following talk in Weber 117
Host: Michael Kirby

Title: The algebraic geometry of persistence barcodes

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.

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