BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Relative cluster categories and Higgs categories with infinite-dim
 ensional morphism spaces. - Yilin Wu (Université Paris 7 - Denis-Diderot\
 , East China Normal University)
DTSTART:20211126T160000Z
DTEND:20211126T170000Z
UID:TALK164911@talks.cam.ac.uk
DESCRIPTION:Cluster categories were introduced in 2006 by Buan-Marsh-Reine
 ke-Reiten-Todorov in order to categorify acyclic cluster algebras without 
 coefficients. Their construction was generalized by Amiot to Jacobi-finite
  quiver with potential (2009). Later\, Plamondon generalized it to arbitra
 ry cluster algebras associated with quivers (2009 and 2011). Cluster algeb
 ras with coefficients are important since they appear in nature as coordin
 ate algebras of varieties like Grassmannians\, double Bruhat cells\, unipo
 tent cells\,... The work of Geiss-Leclerc-Schr&ouml\;er often yields Frobe
 nius exact categories which allow to categorify such cluster algebras. In 
 previous work\, we have constructed Higgs categories and relative cluster 
 categories in the Jacobi-finite setting (arXiv:2109.03707). Higgs categori
 es generalize the Frobenius categories used by Geiss-Leclerc-Schr&ouml\;er
 .\nIn this talk\, we will present the construction of the Higgs category a
 nd of the relative cluster category in the Jacobi-infinite setting. As in 
 the Jacobi-finite case\, the Higgs category is no longer exact but still e
 xtriangulated in the sense of Nakaoka-Palu (2019). We will also give the c
 onstruction of a cluster character in this setting.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR