The following K-quid seminar will be motivated by the Atiyah-Singer index theorem. We will not discuss the meaning of each term appearing in the statement. Our purpose will be to use this theorem to introduce the index as a link between operator theory and geometry.
First we will define the index of a Fredholm operator and we will enounce some of its properties which make it interesting. Then we will briefly introduce the K-theory of C*-algebras and how this theory provide a new framework to compute indices more efficiently.
Eventually we will determine a "pre Atiyah-Singer theorem" in an easier case where every quantity is computable.
