Speaker
Description
Under mirror symmetry, deformation classes of Fano varieties are associated to mutation classes of maximally mutable Laurent polynomials (MMLPs). We expect birational relationships between the general members of two deformation classes to be reflected, in the pair of mirror mutation classes, as combinatorial relationships between two MMLPs.
I will present an alternative construction of a Fano variety that is mirror to a given MMLP, which uses mirror theorems of the Gross-Siebert program. The resulting Fano variety is difficult to describe explicitly. However, when two given MMLPs are related by certain combinatorial conditions, the construction can be extended to include the construction of a birational map between the two Fano varieties produced.
Applying all this to rigid MMLPs in two variables recovers all but one of the blow-ups in the chain of smooth del Pezzo surfaces.
