Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The first thirty years of Andersen-Lempert theory   In this paper we expose the impact of the fundamental discovery, made by Erik
Anders\'en and L\'aszl\'o Lempert in 1992, that the group generated by shears
is dense in the group of holomorphic automorphisms of complex Euclidean spaces
of dimensions $n>1$. In three decades since its publication, their
groundbreaking work led to the discovery of several new phenomena and to major
new results in complex analysis and geometry involving Stein manifolds and
affine algebraic manifolds with many automorphisms. The aim of this survey is
to present some focal points of these developments, with a view towards the
future.

18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs