Professor Carlsson received a Ph.D. in Mathematics from Stanford University in 1976, in the area of algebraic topology. He taught at University of Chicago, University of California (San Diego), Princeton University, and Stanford University, and is currently Professor Emeritus at Stanford University. He has given plenary addresses at the Annual Meetings of the AMS and SIAM, an invited address at the International Congress of Mathematicians, and delivered the Rademacher Lectures at the University of Pennsylvania, the Pitcher Lectures at Lehigh University, and the Wing Lectures at the University of Rochester.
During the first 20 years of his career, he worked exclusively in the core areas of algebraic topology, including homotopy theory, algebraic K-theory, equivariant homotopy theory, and high dimensional manifold topology. Among his achievements are the proof of G.B. Segal’s Burnside Ring Conjecture, a proof of D. Sullivan’s fixed-point conjecture, and extensive work on S.P. Novikov’s conjecture on higher signatures and its analogues.
Since approximately the year 2000, he has been working intensively on the development of Topological Data Analysis, the subject of the present lecture series proposal. As part of that effort, he led two NSF Focused Group efforts, as well as a multi-university DARPA initiative focused on this subject. He is also a founder of Ayasdi Inc., a company which is commercializing a number of these developments.