Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recent progress on rigity properties of higher rank diagonalizable
  actions and applications   The rigidity propeties of higher rank diagonalizable actions is a major theme
in homogenous dynamics, with origins in work of Cassels and Swinnerton-Dyer in
the 1950s and Furstenberg. We survey both results and conjectures regarding
such actions, with emphasize on the applications of these results towards
understanding the distribution of integer points on varieties, quantum unique
ergodicity, and Diophantine approximations.

17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph