Define asymptotic as a class of sequences {$ x_i$},$_{i\in\mathbb N}$ modulo equivalence {$x_i$}={$y_i$} if $\lim_{i\to\infty} (x_i/y_i)=c\in\mathbb R,c\ne 0$. More, we define $X= …

Let $Trop(Gr(m,n))$ denote the tropicalization of the grassmannian $Gr(n,m)$. Let $\phi^m : \mathbb R^{n \choose 2} \rightarrow \mathbb R^{n \choose m}$ such that $X_{i,j} \righta …

To a given a Laurent polynomial $f$ over the field of Puiseux seris with parameter $t$, $f \in \mathbb{C} \lbrace\lbrace t \rbrace\rbrace[z_1^{\pm1},...,z_n^{\pm 1}]$, one can asso …

Edit: I realize the mathematics below is lacking a precise phrasing. I hope that the intuitiion behind the question is clear enough that a reader will understand the question and p …

On Wikipedia there some pictures of two dimensional amoebas (Thanks to Oleg Alexandrov for the pictures and the Matlab code he gives to build them). I was wondering if somewhere …

In this nice paper Mikhalkin uses certain (more geometrical than algebraic) aspects of tropical geometry to prove that every complex projective hypersurface in $\mathbb C \mathbb P …

My excuses in advance in case my question is too vague (which is mainly due to the fact that I'm not really familiar with tropical/toric geometry, but at least I still believe that …

What are some of the important unanswered questions in the field of tropical geometry?

Tropical geometry can be described as "algebraic geometry" over the semifield $\mathbb{T}$ of tropical numbers. As a set, $\mathbb{T}=\mathbb{R}\cup { -\infty}$; this is endowed wi …

Hello, in G. Mikhalkin's Papaer "DECOMPOSITION INTO PAIRS-OF-PANTS FOR COMPLEX ALGEBRAIC HYPERSURFACES": http://arxiv.org/pdf/math/0205011.pdf There is a lemma about the relation b …

I often hear people speaking of the many connections between algebraic varieties and tropical geometry and how geometric information about a variety can be read off from the associ …

I'm interested in learning tropical geometry. But my background in algebraic geometry is limited. I know basic facts about varieties in affine and projective space, but nothing abo …

I'm a beginner in tropical geometry, and I'm running into the following question: In the usual polynomial ring over a field, one has algorithms (i.e. using a Groebner basis) for d …

Many concepts is algebraic geometry have tropical analogues. Question: Is there an analogue of the weight filtration or Hodge filtration for tropical varieties? A tropical curv …

One of the motivations to study tropical geometry is that there are some hard Algebraic Questions that can be answered by proving them in the Tropical World. For example one can sh …