On zeros of multilinear polynomials (Max Forst, CGU)

Consider rational polynomials in multiple variables that are linear with respect to some of the variables. In this talk we discuss the problem of finding a zero of such polynomials that are bounded with respect to a height function. For a system of such polynomials satisfying certain technical conditions we prove the existence of a bounded height simultaneous zero. For a single such polynomial we prove the existence of a zero of bounded height lying outside of a prescribed algebraic set. Based on joint work with Lenny Fukshansky.