Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degenerate Riemann-Hilbert-Birkhoff problems, semisimplicity, and
  convergence of WDVV-potentials   In the first part of this paper, we give a new analytical proof of a theorem
of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb
P^1$ with coalescing irregular singularities of Poincar\'e rank 1, and
generalizing a previous result of B. Malgrange. In the second part of this
paper, as an application, we prove that any semisimple formal Frobenius
manifold (over $\mathbb C$), with unit and Euler field, is the completion of an
analytic pointed germ of a Dubrovin-Frobenius manifold. In other words, any
formal power series, which provides a quasi-homogenous solution of WDVV
equations and defines a semisimple Frobenius algebra at the origin, is actually
convergent under no further tameness assumptions.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th