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Symplectic topology of K3 surfaces via mirror symmetry

Presented by: 
Ivan Smith University of Cambridge
Date: 
Friday 18th August 2017 - 16:00 to 17:00
Venue: 
INI Seminar Room 1
Abstract: 
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons