Description
I will introduce a version of the mixed volume of lattice polytopes taking values in Z/2Z (very differently from the usual mixed volume modulo 2). It comes from arithmetic geometry, is constructed using tropical techniques, and appears in real algebraic geometry whenever the usual mixed volume appears over the complex numbers. For instance, it governs the parity of roots with the negative first coordinate for generic real sparse systems of equations (while the total number of roots is governed by the usual mixed volume) and defines the signs of the leading coefficients of sparse resultants.
