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SUMMARY:Daniel Labardini-Fragoso (UNAM)
DTSTART:20221107T130000Z
DTEND:20221107T140000Z
DTSTAMP:20260710T044509Z
UID:paris-algebra-seminar/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/paris-algebr
 a-seminar/100/">Revisiting Derksen-Weyman-Zelevinsky's mutations</a>\nby D
 aniel Labardini-Fragoso (UNAM) as part of Paris algebra seminar\n\nLecture
  held in room 01 of the Institut Henri Poincaré\, Paris\, France.\n\nAbst
 ract\nThe mutation theory of quivers with potential and their representati
 ons\, developed around 15 years ago by Derksen-Weyman-Zelevinsky\, has had
  a profound impact both inside and outside the theory of cluster algebras.
  In this talk I will present results obtained in joint works with Geiss an
 d Schröer\, and with de Laporte\, about some interesting behaviors of DWZ
 's mutations of representations. Namely\, despite needing several non-cano
 nical choices of linear-algebraic data in order to be performed\, they can
  always be arranged so as to become regular maps on dense open subsets of 
 representation spaces rep(Q\,S\,d). As a consequence\, one obtains the inv
 ariance of Geiss-Leclerc-Schröer's 'generic basis' under mutations even i
 n the Jacobi-infinite case\, thus generalizing a result of Plamondon. Furt
 hermore\, given two distinct vertices k\, \\ell of a quiver with potential
  (Q\,S)\, the k-th mutation of representations takes the \\ell-th indecomp
 osable projective over (Q\,S) to the \\ell-th indecomposable projective ov
 er \\mu_k(Q\,S). When a certain 'optimization' condition is satisfied by \
 \ell\, this allows to compute certain 'Landau-Ginzburg potentials' as F-po
 lynomials of projective representations.\n\nIn-person talk at the room 01 
 of the Institut Henri Poincaré\, Paris\, France\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/100/
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