Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A multi-dimensional resolution of singularities with applications to
  analysis   We formulate a resolution of singularities algorithm for analyzing the zero
sets of real-analytic functions in dimensions $\geq 3$. Rather than using the
celebrated result of Hironaka, the algorithm is modeled on a more explicit and
elementary approach used in the contemporary algebraic geometry literature. As
an application, we define a new notion of the height of real-analytic
functions, compute the critical integrability index and obtain the sharp growth
rate of sublevel sets. This also leads to a characterization of the oscillation
index of scalar oscillatory integrals with real-analytic phases in all
dimensions.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess