Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kontsevich's deformation quantization: from Dirac to multiple zeta
  values   One way of reconciling classical and quantum mechanics is deformation
quantization, which involves deforming the commutative algebra of functions on
a Poisson manifold to a non-commutative, associative algebra, reminiscent of
the space of quantum observables. This depends on a formal parameter $\hbar$,
so that the original pointwise product is recovered when $\hbar=0$. In 1997
Kontsevich showed that a deformation quantization exists for every Poisson
manifold. He furthermore gave a simple, combinatorial formula for producing a
quantization of any Poisson structure on $\mathbb{R}^n$. The primary aim of
this essay, largely drawn from the author's MMath dissertation at Oxford, is to
present and explain Kontsevich's results. Starting with the motivation, we
discuss how the problem is solved by situating it in a richer mathematical
structure, performing a few original calculations along the way. We hope to
communicate a sense of the strange links between this subject and seemingly
distant areas of mathematics, and also to describe some of the contemporary
research in the field. To these ends, we consider a recent paper,
arXiv:1812.11649 [math.QA], which connects deformation quantization to multiple
zeta values.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: stat
32
The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex