  According to the real \tau-conjecture, the number of real roots of a sum of
products of sparse polynomials should be polynomially bounded in the size of
such an expression. It is known that this conjecture implies a superpolynomial
lower bound on the arithmetic circuit complexity of the permanent.
  In this paper, we use the Wronksian determinant to give an upper bound on the
number of real roots of sums of products of sparse polynomials. The proof
technique is quite versatile; it can in particular be applied to some sparse
geometric problems that do not originate from arithmetic circuit complexity.
The paper should therefore be of interest to researchers from these two
communities (complexity theory and sparse polynomial systems).
