Amoebas and tropical geometry

This web page highlights some of the conjectures and open problems concerning Amoebas and tropical geometry.

If you would like to print a hard copy of the whole outline, you can download a dvi, postscript or pdf version.

A list of participants is available.

You may also wish to view the homework from Bernd Sturmfels.

1. Open problems
1. Combinatorics of linear tropical varieties
2. Monge-Amp\`{e}re measure and mixed cells
3. Membership problems
4. Recognition problems
5. Half-space behavior of amoebas
6. Higher order connectedness of amoebas
7. What does the Riemann-Roch theorem say in the tropical world?
8. Tropical Calabi-Yau manifolds and tropical line bundles
9. Real tropical varieties
10. The tropical Grassmannian
11. Real Gromov-Witten invariants and tropical geometry
12. Idempotent geometry
13. Moduli space of holomorphic polygons
14. Solidness of amoebas of maximally sparse polynomials
15. Topology of amoebas of linear spaces
16. Nullstellensatz for amoebas
17. Tropical Calabi-Yau structures
18. Contour of an amoeba
19. Tropical bases
20. Real enumerative invariants
21. Positive tropical varieties and cluster algebras
22. Statistical algebraic geometry
23. Compact tropical varieties, Monge-Amp\`{e}re equation, Calabi conjecture and curve counting
2. Snapshot of the pre-open problem session
3. Snapshot of the open problem session
1. Relevant lines of research
2. Basic definitions
3. Computational issues
4. Recognition problems
5. Applications

There is also a photograph of the white board from one of the discussion sessions.

The individual participant contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.