Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quelques probl\`emes de g\'eom\'etrie \'enum\'erative, de matrices
  al\'eatoires, d'int\'egrabilit\'e, \'etudi\'es via la g\'eometrie des
  surfaces de Riemann   Complex analysis is a powerful tool to study classical integrable systems,
statistical physics on the random lattice, random matrix theory, topological
string theory,... All these topics share certain relations, called "loop
equations" or "Virasoro constraints". In the simplest case, the complete
solution of those equations was found recently: it can be expressed in the
framework of differential geometry over a certain Riemann surface which depends
on the problem : the "spectral curve". This thesis is a contribution to the
development of these techniques, and to their applications. Keywords: random
matrices, random maps, integrable systems, algebraic geometry, loop equations,
topological recursion, Hurwitz numbers, Gromov-Witten invariants, Tracy-Widom
laws, beta ensemble, large N asymptotics in random matrix theory.

35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
16
The categories of this paper are: stat