Pure PGR Seminar - The combinatorial Laplace operator on simplicial complexes, Fabio Strazzeri, Southampton Seminar

Event details

The Laplacian operator is a well-known differential operator given by the divergence of the gradient of a function f and it has been used in different physical phenomena. Its discrete counterpart has been defined for weighted graphs and gives useful insight on their geometry. In this talk I will introduce it and explain how it can be generalised in higher dimension, as Horak and Just did, for finite simplicial complexes. I will then talk a bit about how this higher dimensional Laplacian gives information on the homology of a simplicial complex and how it behaves when we delete or collapse simplices. Time permitting I will also sketch how Morse theory intersect with such discrete operator.