Abstract

This will be the first of two talks about non-commutative geometry, where the second will be given by visiting PhD student Ada Masters. In this talk we will start of with the circle and its connection to the group algebra of the integers through Fourier series. Adding another circle, we obtain the torus and disturbing their interaction through a (irrational) rotation we arrive at the non-commutative torus. In this abstract setting we will also talk about differentiation and smooth structure.