Algebraic and Combinatorial Aspects of Tropical Geometry

ISBN-13: 9780821891469 / Angielski

Opis

This volume contains the proceedings of the CIEM workshop on Tropical Geometry, held December 12-16, 2011, at the International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain. Tropical geometry is a new and rapidly developing field of mathematics which has deep connections with various areas of mathematics and physics, such as algebraic geometry, symplectic geometry, complex analysis, dynamical systems, combinatorics, statistical physics, and string theory. As reflected by the content of this volume, this meeting was mainly focused on the geometric side of the tropical world with an emphasis on relations between tropical geometry, algebraic geometry, and combinatorics. This volume provides an overview of current trends concerning algebraic and combinatorial aspects of tropical geometry through eleven papers combining expository parts and development of modern techniques and tools.

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Table of Contents:<ul><li>Intersection multiplicity numbers between tropical hypersurfaces by B. Bertrand and F. Bihan</li><li>On the total curvature of tropical hypersurfaces by B. Bertrand, L. L. de Medrano, and J.-J. Risler </li><li>Tropical Teichmuller and Siegel spaces by M. Chan, M. Melo, and F. Viviani </li><li>Elliptic curves in honeycomb form by M. Chan and B. Sturmfels </li><li>Tropically unirational varieties by J. Draisma and B. Frenk </li><li>A guide to tropicalizations by W. Gubler </li><li>Categorical notions of layered tropical algebra and geometry by Z. Izhakian, M. Knebusch, and L. Rowen </li><li>Tropical realization spaces for polyhedral complexes by E. Katz </li><li>Local tropicalization by P. Popescu-Pampu and D. Stepanov</li><li>Some acyclic systems of permutations are not realizable by triangulations of a product of simplices by F. Santos </li><li>Tropical $(1,1)$-homology for floor decomposed surfaces by K. M. Shaw </li></ul>