Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Negative definite functions and a dynamical characterization of property
  (T) for countable groups   A class of negative definite kernels is defined in terms of measure spaces.
Using this concept, property (T) for a countable group $\G$ is characterized in
terms of measure preserving actions of $\G$, as follows. If a set $S$ is
translated a finite amount by any fixed element of $\G$, then there is a
uniform bound on how far $S$ is translated.

29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph