On October 21, 2014, the Department of Mathematics hosted a colloquium for Professor Gunnar Carlsson, Stanford University. Prof. Carlsson was invited to the CSU campus by ISTeC (The Information Science and Technology Center) as 1 of 4 Distinguished Lectures held during the Fall 2014 semester. While visiting, Prof. Carlsson spoke at the Mathematics Departmental Colloquium. The title of his talk, The algebraic geometry of persistence barcodes, was presented. The abstract included the following: 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.
Gunnar Carlsson holds a B.A. Harvard 1973 and a Ph.D. Stanford 1976. He currently holds a position as the Ann and Bill Swindell's Professor at Stanford University. He has worked in various areas of homotopy theory, equivariant algebraic topology, and algebraic Ktheory. He proved Segal's Burnside Conjecture as well a Sullivan's fixed point conjecture. Prof. Carlsson 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 also led a multiuniversity DARPA initiative on this topic.
