Fano Polytopes are a family of integral lattice polytopes with important applications in Toric Geometry. Recent results in Mirror Symmetry  showed that it is possible to find deformation-equivalent families of Fano varieties by computing some Laurent polynomials, called Maximally-Mutable Laurent Polynomials , which are naturally associated to Fano Polytopes.
In this talk, I will illustrate the main challenges and the algorithms involved in the computation of Maximally-Mutable Laurent Polynomials for some families of Fano Polytopes in three dimensions.
I will also discuss the role of Machine Learning algorithms both for tuning the algorithm's parameters and for exploring the database of Maximally-Mutable Laurent Polynomials.
This is a joint work with Tom Coates and Alexander Kasprzyk.