Brownian Motion and Index Formulas for the de Rham Complex (Mathematical Research)

This book is an easy-to-read reference providing a link between partial differential equations (pde), stochastic analysis, and index theory. Most mathematicians working in pde are only vaguely familiar with the powerful ideas of stochastic analysis. On the other hand, the additional intuition which Taira´s book conveys might provide better insight and be helpful for their work.
In addition, the book provides a nice compendium for a large variety of facts from differential geometry, functional analysis, pseudodifferential operators, and Markov processes - for quickly looking up a theorem.