The Ronkin function and the Ronkin measure

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Speaker:

Johannes Lundqvist (U Stockholm)

Abstract:

The Ronkin function of a polynomial LaTeX: f is closely connected to the amoeba of LaTeX: f. It has for example been used by Passare and Rullgård to prove an important result about the combinatorial structure of the amoeba. By taking the real Monge-Ampère measure of the Ronkin function we get a positive measure, with support on the amoeba, called the Ronkin measure. The Ronkin measure is rather well understood in the two variable case. However, not much is known in the higher dimensional case.

In this talk we study the special case of an affine linear polynomial in three variables.

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