Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological expansion of the Bethe ansatz, and non-commutative algebraic
  geometry   In this article, we define a non-commutative deformation of the "symplectic
invariants" of an algebraic hyperelliptical plane curve. The necessary
condition for our definition to make sense is a Bethe ansatz. The commutative
limit reduces to the symplectic invariants, i.e. algebraic geometry, and thus
we define non-commutative deformations of some algebraic geometry quantities.
In particular our non-commutative Bergmann kernel satisfies a Rauch variational
formula. Those non-commutative invariants are inspired from the large N
expansion of formal non-hermitian matrix models. Thus they are expected to be
related to the enumeration problem of discrete non-orientable surfaces of
arbitrary topologies.

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The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga