
Density of Fibers for the Filtered Fukaya Category of a Cotangent Bundle
Stéphane Guillermou of Nantes Université presents a research seminar talk in the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar series, addressing how a cotangent bundle's wrapped Fukaya category relates to its filtered counterpart. He opens with Abouzaid's established result that a single cotangent fiber generates the wrapped Fukaya category, then shows this generation fails once the category is filtered. Working instead with the interleaving distance that filtered Fukaya categories carry, he proves that iterated cones built from cotangent fibers generate a dense subcategory rather than the whole category. The argument proceeds through an embedding of the Fukaya category into the category of sheaves, and the result settles a question originally posed by Biran, who had obtained a separate proof together with Ambrosioni and Cornea. The talk, drawn from joint work with Claude Viterbo and Bingyu Zhang, runs 79 minutes and assumes graduate-level familiarity with symplectic geometry and category theory throughout.