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math.AG2018★ 5 cited
The tropical analogue of the Helton-Nie conjecture is true
Xavier Allamigeon, Stéphane Gaubert, Mateusz Skomra
Helton and Nie conjectured that every convex semialgebraic set over the field of real numbers can be written as the projection of a spectrahedron. Recently, Scheiderer disproved th…
math.AG2016★ 30 cited
Tropical spectrahedra
Xavier Allamigeon, Stéphane Gaubert, Mateusz Skomra
We introduce tropical spectrahedra, defined as the images by the nonarchimedean valuation of spectrahedra over the field of real Puiseux series. We provide an explicit polyhedral c…