Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a conjecture of Sokal concerning roots of the independence polynomial   A conjecture of Sokal (2001) regarding the domain of non-vanishing for
independence polynomials of graphs, states that given any natural number
$\Delta \ge 3$, there exists a neighborhood in $\mathbb C$ of the interval $[0,
\frac{(\Delta-1)^{\Delta-1}}{(\Delta-2)^{\Delta}})$ on which the independence
polynomial of any graph with maximum degree at most $\Delta$ does not vanish.
We show here that Sokal's Conjecture holds, as well as a multivariate version,
and prove optimality for the domain of non-vanishing. An important step is to
translate the setting to the language of complex dynamical systems.

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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin