Different Faces of Geometry, Softcover reprint of the original 1st ed. 2004 International Mathematical Series, Vol. 3

This volume presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: Amoebas and Tropical Geometry, Convex Geometry and Asymptotic Geometric Analysis, Differential Topology of 4-Manifolds, 3-Dimensional Contact Geometry, Floer Homology and Low-Dimensional Topology, Kähler Geometry, Lagrangian and Special Lagrangian Submanifolds, Refined Seiberg-Witten Invariants. These apparently diverse topics have a common feature in that they are all areas of exciting current activity.

Refined Seiberg-Witten Invariants.- 3-Dimensional Methods in Contact Geometry.- Asymptotic Convex Geometry Short Overview.- Singularities of Special Lagrangian Submanifolds.- Curvature Functionals, Optimal Metrics, and the Differential Topology of 4-Manifolds.- Amoebas of Algebraic Varieties and Tropical Geometry.- Heegaard Diagrams and Holomorphic Disks.- Exact Lagrangian Submanifolds in T*Sn and the Graded Kronecker Quiver.- The Construction Problem in Kähler Geometry.