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SUMMARY:Fan Qin/覃帆 (Shanghai Jiao Tong University)
DTSTART:20201227T083000Z
DTEND:20201227T091500Z
DTSTAMP:20260423T024028Z
UID:iccm2020/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/iccm2020/11/
 ">Dual canonical bases and cluster algebras</a>\nby Fan Qin/覃帆 (Shangh
 ai Jiao Tong University) as part of ICCM 2020\n\n\nAbstract\nOne of Fomin 
 and Zelevinsky’s main motivations for cluster algebras was to study the 
 dual canonical bases. Correspondingly\, it had been long conjectured that 
 the quantum cluster monomials (certain monomials of generators) belong to 
 the dual canonical bases up to scalar multiples. In a geometric framework 
 for cluster algebras\, Fock and Goncharov expected that cluster algebras p
 ossess bases with good tropical properties. In this talk\, we consider a l
 arge class of quantum cluster algebras called injective-reachable (equival
 ently\, there exists a green to red sequence). We study their tropical pro
 perties. Then we introduce the (common) triangular basis\, which is a Kazh
 dan-Lusztig type basis with good tropical properties. We verify the above 
 motivational conjecture in full generality.\n
LOCATION:https://researchseminars.org/talk/iccm2020/11/
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