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Maxim Jeffs - Functoriality for Fukaya categories of very affine hypersurfaces
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October 14, 1 pm ET: Maxim Jeffs (Harvard) - Functoriality for Fukaya categories of very affine hypersurfaces
Abstract: A very affine hypersurface is the vanishing locus of a Laurent polynomial inside a complex torus; its complement is also a very affine hypersurface, in one of two subtly-different ways. The (partially) wrapped Fukaya categories of the hypersurface and its complement are closely related: Auroux sketched the definitions of several new acceleration and restriction functors between them. I'll explain how we can define these functors in terms of gluings of Liouville sectors and how this implies conjectures of Auroux about their mirror counterparts, building on work of Gammage-Shende. On the way, I'll explain how the different realizations of the complement lead to very different Fukaya categories, related by a non-geometric equivalence mediated by derived Knorrer periodicity. This is joint work with Benjamin Gammage.
Questions
00:28:03 Yoon Jae Nho: which direction of infinity?
00:29:23 Yoon Jae Nho: why would the end not be singular?
00:29:44 Yoon Jae Nho: for the restriction functor?
01:07:48 Yoon Jae Nho: just to clarify, does the necessity to use derived scheme still appear when you use the \eta_{\infty}-grading as well?
Abstract: A very affine hypersurface is the vanishing locus of a Laurent polynomial inside a complex torus; its complement is also a very affine hypersurface, in one of two subtly-different ways. The (partially) wrapped Fukaya categories of the hypersurface and its complement are closely related: Auroux sketched the definitions of several new acceleration and restriction functors between them. I'll explain how we can define these functors in terms of gluings of Liouville sectors and how this implies conjectures of Auroux about their mirror counterparts, building on work of Gammage-Shende. On the way, I'll explain how the different realizations of the complement lead to very different Fukaya categories, related by a non-geometric equivalence mediated by derived Knorrer periodicity. This is joint work with Benjamin Gammage.
Questions
00:28:03 Yoon Jae Nho: which direction of infinity?
00:29:23 Yoon Jae Nho: why would the end not be singular?
00:29:44 Yoon Jae Nho: for the restriction functor?
01:07:48 Yoon Jae Nho: just to clarify, does the necessity to use derived scheme still appear when you use the \eta_{\infty}-grading as well?
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