Tropical Geometry, Amoebas and Polytopes

January 15 - April 30, 2018

Tropical geometry is a fast growing field at the interface between algebraic geometry and combinatorics with deep connections to many branches of pure mathematics, applied mathematics, and physics.

Algebraic varieties can be logarithmically degenerated to tropical varieties, which are polyhedral complexes satisfying certain combinatorial properties. At any intermediate stage before reaching its final limit, the degeneration process yields a structure known as an amoeba. Both tropical varieties and amoebas are dual to subdivisions of polytopes, and this leads to an infusion of combinatorial methods into algebraic, complex-analytic, and non-Archimedean geometry.

In our programme, we plan to focus on tropical algebra and applications; combinatorics, polytopes, and complexity; moduli spaces of curves and mirror symmetry; and tropical geometry and amoebas in higher dimension.

Scientific Advisory Board: Mark Gross (Cambridge), Ilia Itenberg (Paris), Michael Joswig (Berlin), Grigory Mikhalkin (Geneva), Bernd Sturmfels (Berkeley)


Workshop on Tropical algebra and applications, Jan 22-26

Workshop on Combinatorics, polytopes, and complexity, Feb 19-23

Workshop on Moduli spaces of curves and mirror symmetry, March 19-23

Workshop on Tropical varieties and amoebas in higher dimension, April 16-20 This conference is sponsored by the Simons Foundation.



  1. Tropicalized quartics and canonical embeddings for tropical curves of genus 3 - Marvin Anas Hahn Hannah Markwig Yue Ren Ilya Tyomkin
  2. Stillman's conjecture via generic initial ideals - Jan Draisma Michal Lason Anton Leykin
  3. Algorithms for Tight Spans and Tropical Linear Spaces - Simon Hampe Michael Joswig Benjamin Schröter
  4. Realization spaces of matroids over hyperfields - Emanuele Delucchi Linard Hoessly Elia Saini
  5. Describing Amoebas - Mounir Nisse Frank Sottile
  6. Polynomials and tensors of bounded strength - Arthur Bik Jan Draisma Rob H. Eggermont
  7. Real tropicalization and analytification of semialgebraic sets - Philipp Jell Claus Scheiderer Josephine Yu
  8. Counts of (tropical) curves in E×P^1 and Feynman integrals - Janko Böhm Christoph Goldner Hannah Markwig
  9. Tropical Mirror Symmetry in Dimension One - Janko Böhm Christoph Goldner Hannah Markwig
  10. Lefschetz (1,1)-theorem in tropical geometry - Philipp Jell Johannes Rau Kristin Shaw
  11. The algebraic boundary of the sonc cone - Jens Forsgård Timo de Wolff
  12. Higher Connectivity of Tropicalizations - Diane Maclagan Josephine Yu
  13. Tropical Carathéodory with Matroids - Georg Loho Raman Sanyal