| ABSTRACT |
What is good mathematics? Should it be difficult by using technical arguments, should it be fancy by using advanced theories, or all these do not matter and should it have practical applications? In this talk for pedestrians, I am going to lead you to one of good mathematics and explain why it is good. The talk could be viewed as a brief introduction to category theory, as I shall explain what a category, a functor, and a natural transformation between two functors are in a way that leads to a statement of an elementary but a deep theorem proved by K. J?nich and M. Atiyah in the sixties that the space of homotopy classes of maps into the space of Fredholm operators on the Hilbert space is naturally isomorphic to the complex K-theory. I will then introduce a work in progress proving a twisted variant of this theorem. The talk is going to be accommodating non-experts and mostly self-contained. |
