Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wall-Crossing implies Brill-Noether. Applications of stability
  conditions on surfaces   Over the last few years, wall-crossing for Bridgeland stability conditions
has led to a large number of results in algebraic geometry, particular on
birational geometry of moduli spaces.
  We illustrate some of the methods behind these result by reproving
Lazarsfeld's Brill-Noether theorem for curves on K3 surfaces via wall-crossing.
We conclude with a survey of recent applications of stability conditions on
surfaces.
  The intended reader is an algebraic geometer with a limited working knowledge
of derived categories. This article is based on the author's talk at the AMS
Summer Institute on Algebraic Geometry in Utah, July 2015.

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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol