28 nov 2023 -- 09:30

**Abstract.**

The Combinatorial Morse Theory is a central tool in combinatorial algebraic topology and it is becoming more and more interesting especially for people working on Topological Data Analysis. In this talk we will present an example of a successful application of the combinatorial Morse theory to a known CW complex S in order to get an explicit combinatorial gradient vector field over S and the associated minimal algebraic complex MS. More in detail, S is the Salvetti's compex which gives the homotopy type of the complement to a complexified real arrangement of hyperplanes and the minimal algebraic complex MS computes the local system cohomology of the complement by means of a boundary operator which is effectively computable.