Joint Colloquium There will be no joint colloquium this week, however for next week we have a fabulous speaker: Friday, September 4 Carslaw 275, 2 PM Alan McIntosh, CMA, ANU, Canberra The Kato square root problem - a new approach with applications to boundary value problems. We will be taking Alan to lunch, leaving from the outside foyer on the 2nd floor of Carslaw at 12:30 PM About 1960 Tosio Kato, during his investigation of the evolution of physical systems, was led to pose a key question about the square root of non-symmetric divergence form elliptic partial differential operators. The one-dimensional problem was solved by Coifman, Meyer and myself in 1982, while it was only in 2001 that the question was fully answered by Auscher, Hofmann, Lacey, Tchamitchian and myself. A more general viewpoint was subsequently provided in joint work of mine with Axelsson and Keith. Recently, these ideas have been employed to give conditions for solvability of some elliptic PDE’s with square integrable boundary values. I shall survey these applications of harmonic analysis to the study of elliptic PDE’s, and present new results of Auscher, Axelsson and myself.