Mukai has introduced a geometric program to reconstruct a K3 surface from a curve on that surface. The idea is to first consider a Brill-Noether locus of vector bundles on the curve. Then the K3 surface containing the curve can be obtained uniquely as a Fourier-Mukai partner of the Brill-Noether locus. In this talk, I will explain how wall-crossing with respect to Bridgeland stability conditions implies that the Mukai's strategy works for curves of genus greater than 12 or genus 11. |

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