Atiyah Singer Theorem

This volume of the EMS contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples.

Vijay Kumar Patodi was a brilliant Indian mathematician who made, during his short life, fundamental contributions to the analytic proof of the index theorem and to the study of differential geometric invariations of manifolds.