Event № 1073
One of the key problems of differential geometry is that a real life manifold, given to us in a digital form, is rarely smooth. Instead, we obtain it often as a polyhedral approximation, which makes computation of interesting invariants a tricky problem, and prompted the creation of various approaches following Cheeger, Gelfand and MacPherson.
I will survey some problems and developments that arise from forcing such smooth notions on combinatorial structures, as well as some interesting results developped from this analogy. Finally, I will discuss how combinatorial intersection theory allows for the definition of a polyhedral de Rham theory, and sketch relations to the Singer conjecture.
A zoom Colloquium, Note the special time: 16:30.