Seminarium KMMF "Teoria Dwoistości"

I begin by describing the various classical index theorems andtheir unified proof(s) by Atiyah and Singer. Then I will show how theabstract framework of one of these proofs led to noncommutative geometry,in the sense of Alain Connes.The story comes full circle when the local index formula in noncommutative geometryis employed to give new proofs of the Atiyah-Singer theorem, and provide nontrivialgeneralisations.