BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Peigen Cao (USTC Hefei) DTSTART:20260209T130000Z DTEND:20260209T140000Z DTSTAMP:20260710T050622Z UID:paris-algebra-seminar/218 DESCRIPTION:Title: The tropical invariant and the $F$-invariant in cluster al gebras\nby Peigen Cao (USTC Hefei) as part of Paris algebra seminar\n\ n\nAbstract\nThe Lambda-invariant and the d-invariant are two integer-valu ed invariants introduced by Kang-Kashiwara-Kim-Oh and by Kashiwara-Kim-Oh- Park in their study of monoidal categorification of cluster algebras using finite-dimensional modules over quiver Hecke algebras and quantum affine algebras. The Lambda-invariant can be viewed as a monoidal categorificatio n of the compatible Poisson structure on those cluster algebras. The d-inv ariant is defined as half the symmetrized sum of Lambda-invariants\, and i t can be used to characterize the strong commutativity between real simple s.\n\n\nIn this talk\, we introduce the tropical invariant and the F-invar iant in cluster algebras. The tropical invariant is defined for any cluste r algebra with a compatible Poisson structure and it generalizes the Lambd a-invariant. The F-invariant is defined as the symmetrized sum of the trop ical invariants and it simultaneously generalizes all of the following inv ariants: the d-invariant\, Derksen-Weyman-Zelevinsky’s E-invariant\, Fu- Gyoda’s f-compatibility degree\, Fomin-Zelevinsky’s compatibility degr ee\, and Qiu-Zhou’s f-intersection number on marked surfaces.\n\nThis ta lk will take place on Zoom only.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/218/ END:VEVENT END:VCALENDAR