Algebraic Invariants of Oil & Vinegar quadratic systems

The problem of solving multivariate polynomial systems is one of the hard problems that have been used to build quantum-resistant cryptosystems. 

In the modern literature, to measure the complexity of solving multivariate systems, various authors have introduced quantities associated with different algebraic properties: the first fall degree that is related to the computation of the syzygies of the system, the degree of regularity that is computed through the Hilbert series, and the solving degree that arises from Gröbner bases. 

In this seminar, we investigate these algebraic invariants for Oil and Vinegar quadratic systems and for a new class of quadratic systems, called mixed systems, made by Oil and Vinegar equations and generic quadratic equations.