Invited talk to the Second Congress of Greek Mathematicians (SCGM 2022), 04-08 July (Athens). My talk will take place on 06 July of 2022.

Conference webpage: SCGM 2022

Title: Quadratic robust and generalized robust toric ideals of graphs

(joint work with Ignacio Garcia-Marco)

Abstract: A toric ideal is called robust if its universal Gröbner basis is a minimal set of generators, and is called generalized robust if its universal Gröbner basis equals its universal Markov basis (the union of all its minimal sets of binomial generators). Robust and generalized robust toric ideals are both interesting from both a Commutative Algebra and an Algebraic Statistics perspective. However, only a few nontrivial examples of such ideals are known. In this talk we study these properties for toric ideals of graphs. We characterize combinatorially the graphs giving rise to robust and to generalized robust toric ideals generated by quadratic binomials.