The logarithm map from complex algebraic torus to the Euclidean space, sends an n-tuple of nonzero complex numbers to the logarithms of their absolute values. The image of a subvariety in the torus under the logarithm map is called "amoeba" and it contains geometric information about the variety. In this talk we explore the extension of the notion of logarithm map and amoeba to the non-commutative setting, that is for a spherical homogeneous space G/H where G is a connected complex reductive algebraic group. This is related to Victor Batyrev's question of describing K-orbits in G/H.

The talk is based on a joint work with Victor Batyrev, Megumi Harada and Johannes Hofscheier.