Title: "Polynomial inequalities over a quadratic map with low-dimensional image are easy". D.V. Pasechnik (Univ. Frankfurt, Germany), jointly with E. de Klerk (TU Delft, NL) and D. Grigoriev (IRMAR, Univ. Rennes I, France) Let p_i(Y)>=0 (0R^k a quadratic map, that is, a vector of k quadratic polynomials in n variables. Then the problem of finding an exact solution of the system p_i(Q(X))>=0 (0