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The D-equivalence conjecture of Bondal and Orlov predicts that birational Calabi-Yau
varieties have equivalent derived categories of coherent sheaves. I will explain how
to prove this conjecture for hyperkahler varieties of K3^[n] type (i.e. those that are
deformation equivalent to Hilbert schemes of K3 surfaces). This is joint work with
Junliang Shen, Qizheng Yin, and Ruxuan Zhang.
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