BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daping Weng (Michigan State University) DTSTART:20201118T190000Z DTEND:20201118T200000Z DTSTAMP:20260423T040009Z UID:AG-Davis/9 DESCRIPTION:Title: Augmentations\, Fillings\, and Clusters\nby Daping Weng (Michigan Sta te University) as part of UC Davis algebraic geometry seminar\n\n\nAbstrac t\nA Legendrian link is a 1-dimensional closed manifold that is embedded i n \n$R^3$ and satisfies certain tangent conditions. Rainbow closures of po sitive braids are natural examples of Legendrian links. In the study of Le gendrian links\, one important task is to distinguish different exact Lagr angian fillings of a Legendrian link\, up to Hamiltonian isotopy\, in the \n$R^4$ symplectization. We introduce a cluster K2 structure on the augmen tation variety of the Chekanov-Eliashberg dga for the rainbow closure of a ny positive braid. Using the Ekholm-Honda-Kalman functor from the cobordis m category of Legendrian links to the category of dga’s\, we prove that a big family of fillings give rise to cluster seeds on the augmentation va riety of a positive braid closure\, and these cluster seeds can in turn be used to distinguish non-Hamiltonian isotopic fillings. Moreover\, by rela ting a cyclic rotation concordance on a positive braid closure with the Do naldson-Thomas transformation on the corresponding augmentation variety\, we prove that other than a family of positive braids that are associated w ith finite type quivers\, the rainbow closure of all other positive braids admit infinitely many non-Hamiltonian isotopic fillings. This is joint wo rk with H. Gao and L. Shen.\n LOCATION:https://researchseminars.org/talk/AG-Davis/9/ END:VEVENT END:VCALENDAR