We give a new geometric proof of the classification of T-polygons, a theorem originally due to Kasprzyk, Nill and Prince, using ideas from mirror symmetry. In particular, this gives a completely geometric proof that any two toric ℚ-Gorenstein degenerations of a smooth del Pezzo X surface are connected via trees of rational curves in the moduli space of X.

In this paper we compute the Newton polytope \mathcal{M}_A of the Morse discriminant in the space of univariate polynomials with a given support set A. Namely, we establish a surjection between the set of all combinatorial types of Morse univariate tropical polynomials and the vertices of \mathcal{M}_A.

In this paper we study the computational feasibility of an algorithm to prove orbifold equivalence between potentials describing Landau–Ginzburg models. Through a comparison with state-of-the-art results of Gröbner basis computations in cryptology, we infer that the algorithm produces systems of equations that are beyond the limits of current technical capabilities. As such the algorithm needs to be augmented by ‘inspired guesswork’, and we provide examples of applying this approach.