Hyperplane Arrangements on Tori and Virtual Resolutions of Toric Embeddings

In 1999 Bayer-Popescu-Sturmfels constructed minimal free resolutions of binomial ideals which correspond to the diagonal embeddings of unimodular toric varieties. Such resolutions are significant in algorithms concerning homological algebra and algebraic geometry. In this talk I will tell the story of how researchers from commutative algebra and homological mirror symmetry joined forces to generalize this construction to all smooth projective toric varieties.