BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Naoki Fujita (University of Tokyo) DTSTART:20201119T100000Z DTEND:20201119T110000Z DTSTAMP:20260423T024805Z UID:notts_ag/36 DESCRIPTION:Title: Newton-Okounkov bodies arising from cluster structures\nby Naoki Fuj ita (University of Tokyo) as part of Online Nottingham algebraic geometry seminar\n\n\nAbstract\nA toric degeneration is a flat degeneration from a projective variety to a toric variety\, which can be used to apply the the ory of toric varieties to other projective varieties. In this talk\, we di scuss relations among the following three constructions of toric degenerat ions: representation theory\, Newton-Okounkov bodies\, and cluster algebra s. More precisely\, we construct Newton-Okounkov bodies using cluster stru ctures\, and realize representation-theoretic and cluster-theoretic toric degenerations from this framework. As an application\, we connect two kind s of representation-theoretic polytopes (string polytopes and Nakashima-Ze levinsky polytopes) by tropicalized cluster mutations. We also discuss rel ations with combinatorial mutations which was introduced in the context of mirror symmetry for Fano varieties. More precisely\, we relate dual polyt opes of these representation-theoretic polytopes by combinatorial mutation s. This talk is based on joint works with Hironori Oya and Akihiro Higashi tani.\n LOCATION:https://researchseminars.org/talk/notts_ag/36/ END:VEVENT END:VCALENDAR