Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Act globally, compute locally: group actions, fixed points, and
  localization   Localization is a topological technique that allows us to make global
equivariant computations in terms of local data at the fixed points. For
example, we may compute a global integral by summing integrals at each of the
fixed points. Or, if we know that the global integral is zero, we conclude that
the sum of the local integrals is zero. This often turns topological questions
into combinatorial ones and vice versa. This expository article features
several instances of localization that occur at the crossroads of symplectic
and algebraic geometry on the one hand, and combinatorics and representation
theory on the other. The examples come largely from the symplectic category,
with particular attention to toric varieties. In the spirit of the 2006
International Conference on Toric Topology at Osaka City University, the main
goal of this exposition is to exhibit toric techniques that arise in symplectic
geometry.

1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an