L2

The recent developments of Mathematical Physics have brought very new ideas about the nature of space . I will argue that we have to mix the methods of noncommutative geometry of Alain Connes with the prophetic views of Grothendieck about the so-called motives and their motivic Galois group .
The dream of a "cosmic Galois group" may soon become an established reality .
 

I will give an expository account of Mathai, Melrose, and Singer [math.DG/0402329], explaining how to define the projective Dirac "operator" when the underlying manifold is neither spin nor spin_C, and how to define its analytic index which need not be an integer. Nevertheless, the usual index formulas apply. Professor Singer will be admitted as honorary member of the London Mathematical Society just before his talk.

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