The workshop Tropical Geometry: New Directions was devoted to a wide discussion and exchange of ideas between the leading experts representing various points of view on the subject, notably, to new phenomena that have opened themselves in the course of the last 4 years. This includes, in particular, refined enumerative geometry (using positive integer q-numbers instead of positive integer numbers), unexpected appearance of tropical curves in scaling limits of Abelian sandpile models, as well as

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... a significant progress in more traditional areas of tropical research, such as tropical moduli spaces, tropical homology and tropical correspondence theorems. (2010) : Primary 14-xx (algebraic geometry), Secondary 81Txx (quantum field theory, related classical field theories), 53Dxx (symplectic geometry, contact ge-ometry), 37-xx (dynamical systems and ergodic theory). Mathematics Subject Classification