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7 votes
4 answers
1k views

Origin of tropical mathematics

On Wikipedia, it is claimed without a source that Imre Simon founded tropical mathematics. The first work of his I was able to find on the subject is Limited subsets of a free monoid which uses the ...
4 votes
0 answers
206 views

History of tropical mathematics

This is a follow-up to this question about the origin of tropical mathematics. Are there any articles, websites or books which deal with the history of tropical mathematics? I have been trying to find ...
2 votes
0 answers
103 views

Amoeba for a K3 surface in $\mathbb {CP}^3$

Let $X=X_\Delta$ be the toric variety associated to a reflexive polyhedron $\Delta$. Consider a Calabi-Yau hypersurface $Y\subset X$, and the image of $Y$ under the moment map $\mu:X\to \Delta$ has ...
4 votes
1 answer
230 views

Poles of an integral of a meromorphic function with toric poles

Suppose I have a meromorphic function in several variables $f(x_1,\ldots,x_k,y_1,\ldots,y_m)$ and I want to integrate along the torus $T^m$ given by $|y_1|=\cdots=|y_m|=1$. It is not true in general ...
4 votes
0 answers
164 views

Two variants of the Littlewood-Offord theorem

I found two different looking things being called the Littlewood-Offord theorem, If $\vec{a} \in \mathbb{R}^k \setminus 0$ and $t \in \mathbb{R}$ then there are $O(\frac{2^k}{\sqrt{k}})$ points $x \...
1 vote
0 answers
102 views

Notion of transversality over the field of Puiseux series.

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 associate the ...