SMRI Seminar: Higson -- Scalable Operators

Abstract: The operation of integration is almost - but not quite - the inverse of
differentiation.  In higher dimensions, the problem of determining similar
almost-inverse r elations, involving for instance the Laplace operator or the Dirac
operator, very often on curved spaces, is commonly encountered, and the theory of
pseudodifferential operators was created to solve it.  I shall give an introduction to
the simple, elegant and geometric approach to pseudodifferential operators that was
recently developed by Erik van Erp and Robert Yuncken.  It uses what I call scalable
operators.  The theory of scalable operators offers a convenient and coordinate-free
means of studying algebras of pseudodifferential operators on geometric spaces, as I
shall try to illustrate using the example of symmetric spaces.