Mounir Nisse

Metric Estimates and Membership Complexity for Archimedean Amoebae and Tropical Hypersurfaces

Given any complex Laurent polynomial

Amoebas and Coamoebas of Linear Spaces

f

On the volume of complex amoebas

,

Analytic Varieties with Finite Volume Amoebas are Algebraic

\mathrm{Amoeba}(f)

The phase limit set of a variety

is the image of its complex zero set under the coordinate-wise log absolute value map. We give an efficiently constructible polyhedral approximation,

Non-Archimedean coamoebae

\mathrm{ArchtTrop}(f)

Geometric and Combinatorial Structure of Hypersurface Coamoebas

, of

Maximally Sparse Polynomials have Solid Amoebas

\mathrm{Amoeba}(f)

Higher convexity for complements of tropical varieties

, and derive explicit upper and lower bounds, solely as a function of the number of monomial terms of

GENERALIZED LOGARITHMIC GAUSS MAP AND ITS RELATION TO (CO)AMOEBAS

f