Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matroids, motives and conjecture of Kontsevich   Let G be a finite connected graph. The Kirchhoff polynomial of G is a certain
homogeneous polynomial whose degree is equal to the first betti number of G.
These polynomials appear in the study of electrical circuits and in the
evaluation of Feynman amplitudes. Motivated by work of D. Kreimer and D. J.
Broadhurst associating multiple zeta values to certain Feynman integrals,
Kontsevich conjectured that the number of zeros of a Kirchhoff polynomial over
the field with q elements is always a polynomial function of q. We show that
this conjecture is false by relating the schemes defined by Kirchhoff
polynomials to the representation spaces of matroids. Moreover, using Mnev's
universality theorem, we show that these schemes essentially generate all
arithmetic of schemes of finite type over the integers.

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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: physics