Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse polynomial equations and other enumerative problems whose Galois
  groups are wreath products   We introduce a new technique to prove connectivity of subsets of covering
spaces (so called inductive connectivity), and apply it to Galois theory of
problems of enumerative geometry. As a model example, consider the problem of
permuting the roots of a complex polynomial $f(x) = c_0 + c_1 x^{d_1} + \ldots
+ c_k x^{d_k}$ by varying its coefficients. If the GCD of the exponents is $d$,
then the polynomial admits the change of variable $y=x^d$, and its roots split
into necklaces of length $d$. At best we can expect to permute these necklaces,
i.e. the Galois group of $f$ equals the wreath product of the symmetric group
over $d_k/d$ elements and $\mathbb{Z}/d\mathbb{Z}$. The aim of this paper is to
prove this equality and study its multidimensional generalization: we show that
the Galois group of a general system of polynomial equations equals the
expected wreath product for a large class of systems, but in general this
expected equality fails, making the problem of describing such Galois groups
unexpectedly rich.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga