for his groundbreaking work on singular integral operators leading to their application to important problems in partial differential equations including his proof of uniqueness in the Cauchy problem the Atiyah Singer index theorem and the propagation of singularities in nonlinear equations

Please fix the punctuation.
... for his ground-breaking work on singular integral operators leading to their application to important problems in partial differential equations, including his proof of uniqueness in the Cauchy problem, the Atiyah -Singer index theorem, and the propagation of singularities in nonlinear equations...