The dimension of an amoeba
Amoebas A(X) are images of algebraic varieties X in logarithmic coordinates and were introduced by Gelfand, Kapranov, Zelevinsky in their study of discriminants. From a "tropical" point of view, they appear as intermediate objects during the process of passing from the classical algebraic geometry to the piece-wise linear, combinatorial world of tropical geometry. However, basic properties of amoebas, even their dimensions, are not well-understood. In my talk, I will review some results and present a new formula computing dim(A(X)), settling a conjecture by Nisse and Sottile. As a corollary, this formula implies that the amoeba dimension only depends on the tropicalization/Bergman fan of X. This is joint work with Jan Draisma et Chi Ho Yuen.