Degeneration of spectral sequences and formality of DG algebras associated to Lagrangians in hyperkähler varieties

Moduli and Algebraic Cycles

23 September 15:30 - 16:30

Borislav Mladenov - Imperial College London

Let L be a (spin, compact) Lagrangian in a holomorphic symplectic variety X. Given a square root K_L^(1/2) of the canonical line bundle of L, consider the dga RHom(K_L^1/2,K_L^1/2) in D(X) and the corresponding local-to-global Ext spectral sequence computing its cohomology. I will explain how mirror symmetry and results of Ivan Smith and Solomon–Verbitsky motivate the degeneration of the spectral sequence and prompt the question whether the dga is formal. I will sketch a proof of the degeneration using deformation quantisation and state the formality result. If time allows (which it won't), I'll mention various generalisations to pairs of Lagrangians and A_\inf categories as well as some open questions.

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John Christian Ottem
University of Oslo
Dan Petersen
Stockholm University
David Rydh
KTH Royal Institute of Technology


Dan Petersen


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