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Symplectic topology of K3 surfaces via mirror symmetry

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SYGW05 - Symplectic geometry - celebrating the work of Simon Donaldson

Co-Author: Nick Sheridan (Princeton & Cambridge)

We prove that there are symplectic K3 surfaces for which the Torelli group, of symplectic mapping classes
acting trivially on cohomology, is infinitely generated.  The proof combines homological mirror symmetry for
Greene-Plesser mirror pairs with results of Bayer and Bridgeland on autoequivalence groups of derived categories
of K3 surfaces.  Related ideas in mirror symmetry yield a new symplectic viewpoint on Kuznetsov's K3-category
of a cubic fourfold.

This talk is part of the Isaac Newton Institute Seminar Series series.

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