Marsden Memorial Lecture: Anil Hirani

I will begin with some memories of how Jerry Marsden was as an advisor. In addition to the clarity and creativity of his mathematical thought, what has remained in my memory are his generosity with ideas, kindness as a human being, and his hands-on approach in the many research discussions we had. I will next introduce discrete exterior calculus (DEC) which got its start with Jerry. The remainder of the talk will be about our recent generalization of DEC to vector bundle valued forms using which I will demonstrate the basic ideas of differential geometry on simplicial complexes. I will describe all the ideas using simple examples to make the talk accessible.