turkmath.org

We define a variant of tropical varieties for exponential sums. These polyhedral complexes can be used to approximate, within an explicit distance bound, the real parts of complex zeroes of exponential sums. We also discuss the algorithmic efficiency of tropical varieties in relation to the computational hardness of algebraic sets. Our proof involves techniques from basic complex analysis, inequalities and some recent probabilistic estimates on projections that might be of interest to analyst. This is joint work with Maurice Rojas and Grigoris Paouris.