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SUMMARY:Étienne Ménard (Université de Caen)
DTSTART:20210413T150000Z
DTEND:20210413T160000Z
DTSTAMP:20260423T021141Z
UID:OCAS/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OCAS/26/">Cl
 uster algebra associated to open Richardson varieties : an algorithm to co
 mpute initial seed</a>\nby Étienne Ménard (Université de Caen) as part 
 of Online Cluster Algebra Seminar (OCAS)\n\n\nAbstract\nIn his paper of 20
 16\, Leclerc wanted to study the total nonnegativity criteria on flag vari
 ety in the same way as Fomin and Zelevinsky studied in '99 the total nonne
 gativity on $GL_n(mathbb{R})$ by stratification via double Bruhat cells. I
 n this setting he wanted to study the cluster algebra structure on the ope
 n Richardson varieties stratifying the flag variety.\n\nBut in order to st
 udy this cluster algebra he used an additive categorification of the open 
 Richardson variety $mathcal{R}_{v\,w}$ by the category $mathcal{C}_{v\,w}$
 . He proved that there is a cluster structure (in the sense of Buan\, Iyam
 a\, Reiten\, Scott) but hadn't given a way to explicitly build a seed for 
 this cluster structure.\n\nMy PhD work was to design a prove an algorithm 
 to explictly build such a seed starting from a seed for the cluster struct
 ure on the category $mathcal{C}_wsupset mathcal{C}_{v\,w}$. I will explain
  the principle\, the concrete usage of this algorithm and draw a sketch of
  the proof.\n\nIf time allows it\, I will also introduce the Sage implemen
 tation I have written during my PhD.\n
LOCATION:https://researchseminars.org/talk/OCAS/26/
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