Algebraic and Combinatorial Aspects of Tropical Geometry
About this Title
Erwan Brugallé, Université Pierre et Marie Curie (Paris 6), Paris, France, Mariá Angélica Cueto, Columbia University, New York, NY, Alicia Dickenstein, Universidad de Buenos Aires, Buenos Aires, Argentina, Eva-Maria Feichtner, University of Bremen, Bremen, Germany and Ilia Itenberg, Université Pierre et Marie Curie (Paris 6), Paris, France, Editors
Publication: Contemporary Mathematics
Publication Year 2013: Volume 589
ISBNs: 978-0-8218-9146-9 (print); 978-1-4704-0940-1 (online)
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.
Graduate students and research mathematicians interested in tropical geometry, algebraic geometry, and combinatorics.
Table of Contents
- Benoît Bertrand and Frédéric Bihan – Intersection multiplicity numbers between tropical hypersurfaces
- Benoît Bertrand, Lucía López de Medrano and Jean-Jacques Risler – On the total curvature of tropical hypersurfaces
- Melody Chan, Margarida Melo and Filippo Viviani – Tropical Teichmüller and Siegel spaces
- Melody Chan and Bernd Sturmfels – Elliptic Curves in Honeycomb Form
- Jan Draisma and Bart Frenk – Tropically unirational varieties
- Walter Gubler – A Guide to Tropicalizations
- Zur Izhakian, Manfred Knebusch and Louis Rowen – Categorical Notions ofLayered Tropical Algebra and Geometry
- Eric Katz – Tropical realization spaces for polyhedral complexes
- Patrick Popescu-Pampu and Dmitry Stepanov – Local tropicalization
- Francisco Santos – Some acyclic systems of permutations are not realizable by triangulations of a product of simplices
- Kristin M. Shaw – Tropical $(1,1)$-homology for floor decomposed surfaces