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date: 2022-01-25
tags: [web/quick_notes]
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# 2022-01-25

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## 09:35

The mirror [P=W conjecture](P=W%20conjecture.md) is the refined Hodge number symmetry between a log [Calabi-Yau](Calabi-Yau.md) mirror pair $(U, U^\vee)$. It predicts that the weight filtration on the cohomology $H^\bullet(U)$ is equivalent to the perverse filtration on the cohomology $H^\bullet(U^\vee)$ associated to the mirror Landau-Ginzburg potentials.