BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Fan Qin (ICRA 2020 Award Winner) (Shanghai Jiao Tong University) DTSTART:20201124T080000Z DTEND:20201124T085000Z DTSTAMP:20260419T111920Z UID:icra2020/21 DESCRIPTION:Title: Bases of cluster algebras\nby Fan Qin (ICRA 2020 Award Winner) (Shan ghai Jiao Tong University) as part of ICRA 2020\n\n\nAbstract\nOne of Fomi n and Zelevinsky’s main motivations for cluster algebras was to study th e dual canonical bases. Correspondingly\, it had been long conjectured tha t the quantum cluster monomials (certain monomials of generators) belong t o the dual canonical bases up to scalar multiples. Geiss-Leclerc-Schröer proved an analogous statement that the cluster monomials belong to the dua l semi-canonical bases\, which are examples of generic bases.\n\nIn a geom etric framework for cluster algebras\, Fock and Goncharov expected that cl uster algebras possess bases with good tropical properties.\n\nIn this tal k\, we consider a large class of quantum cluster algebras called injective -reachable (equivalently\, there exists a green to red sequence). We study their tropical properties and obtain the existence of generic bases. Then we introduce the (common) triangular bases\, which are Kazhdan-Lusztig ty pe bases with good tropical properties. We verify the above motivational c onjecture in full generality and\, by similar arguments\, a conjecture by Hernandez-Leclerc about monoidal categorification.\n LOCATION:https://researchseminars.org/talk/icra2020/21/ END:VEVENT END:VCALENDAR