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Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah?Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved...

Aside from the obvious statement that it should be a theory capable of unifying general relativity and quantum field theory, not much is known about the true nature of quantum gravity.

New ideas - and there are many of them for this is an exciting field of research - often diverge to a degree where it seems impossible to decide in which of the many possible direction(s) the ongoing developments should be further sustained.

The division of the book in two (overlapping) parts reflects the duality between the physical vision and the mathematical construction. The former is...