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Lev Rozansky (UNC-CH), Phyiscally Inspired Mathematics Seminar
April 7, 2017 @ 5:20 pm - 6:20 pm
Title: Flag varieties, Hilbert schemes on C^2 and link homology
Abstract: This is a joint work with A. Oblomkov. We construct a categorical action of an ordinary and affine braid group on matrix factorizations over varieties constructed out of Hilbert schemes and flag varieties. The `trace’ of the action of an ordinary braid yields the HOMFLY-PT homology of the link presented by its closure. Our construction should clarify some properties of this homology which look mysterious within the Soergel bimodule based construction. We also expect that this construction fits into the paradigm of geometric Langlands duality and has a direct interpretation within the framework of superstrings/M-theory.