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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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Ivanov's metaconjecture on surface homeomorphisms

Q1. A beautiful survey about these results is the following: McCarthy-Papadopoulos, Simplicial actions of mapping class groups, in Handbook of Teichmüller theory Volume III Q2. Luo's proof of t …
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