The behavior of the norms of roots of univariate trinomials z^{s+t} + pz^t+q in C[z] for fixed support A := {s+t, t, 0} ⊂f2 N with respect to the choice of coefficients p, q ∈f2 C∗f2 is a classical late 19th / early 20th century problem. Although algebraically described by P. Bohl in 1908, the geometry and topology of the corresponding space of coefficients C^A is unknown. We provide such a description yielded by a reinterpretation of this problem in terms of amoeba theory.
The talk is based on joint work with Thorsten Theobald.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/4811