Counting Tropically Degenerate Valuations and p-adic Approaches to the Hardness of the Permanent

Pascal Koiran, Natacha Portier, J. Maurice Rojas

The Shub-Smale Tau Conjecture is a hitherto unproven statement (on integer roots of polynomials) whose truth implies both a variant of $P\ne NP$ (for the BSS model over C) and the…