Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universality and asymptotics of graph counting problems in nonorientable
  surfaces   Bender-Canfield showed that a plethora of graph counting problems in
oriented/unoriented surfaces involve two constants $t_g$ and $p_g$ for the
oriented and the unoriented case respectively. T.T.Q. Le and the authors
recently discovered a hidden relation between the sequence $t_g$ and a formal
power series solution $u(z)$ of the Painlev\'e I equation which, among other
things, allows to give exact asymptotic expansion of $t_g$ to all orders in
$1/g$ for large $g$. The paper introduces a formal power series solution $v(z)$
of a Riccati equation, gives a nonlinear recursion for its coefficients and an
exact asymptotic expansion to all orders in $g$ for large $g$, using the theory
of Borel transforms. In addition, we conjecture a precise relation between the
sequence $p_g$ and $v(z)$. Our conjecture is motivated by the enumerative
aspects of a quartic matrix model for real symmetric matrices, and the analytic
properties of its double scaling limit. In particular, the matrix model
provides a computation of the number of rooted quadrangulations in the
2-dimensional projective plane. Our conjecture implies analyticity of the
$\mathrm{O}(N)$ and $\mathrm{Sp}(N)$-types of free energy of an arbitrary
closed 3-manifold in a neighborhood of zero. Finally, we give a matrix model
calculation of the Stokes constants, pose several problems that can be answered
by the Riemann-Hilbert approach, and provide ample numerical evidence for our
results.

26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess