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SUMMARY:Naoki Fujita (The University of Tokyo)
DTSTART:20210113T010000Z
DTEND:20210113T015000Z
DTSTAMP:20260423T035929Z
UID:LCM2021/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LCM2021/32/"
 >Newton-Okounkov bodies arising from cluster structures and mutations on p
 olytopes</a>\nby Naoki Fujita (The University of Tokyo) as part of Legendr
 ians\, Cluster algebras\, and Mirror symmetry\n\nLecture held in POSTECH\,
  Pohang\, Republic of Korea.\n\nAbstract\nA toric degeneration is a flat d
 egeneration from a projective variety to a toric variety\, which can be us
 ed to apply the theory of toric varieties to other projective varieties. I
 n this talk\, we discuss relations among the following three constructions
  of toric degenerations: representation theory\, Newton-Okounkov bodies\, 
 and cluster algebras. More precisely\, we construct Newton-Okounkov bodies
  using cluster structures\, and realize representation-theoretic and clust
 er-theoretic toric degenerations using this framework. We also discuss its
  relation with combinatorial mutations which was introduced in the context
  of mirror symmetry for Fano varieties. More precisely\, we relate Newton-
 Okounkov bodies of flag varieties arising from cluster structures by combi
 natorial mutations. This talk is based on joint works with Hironori Oya an
 d Akihiro Higashitani.\n
LOCATION:https://researchseminars.org/talk/LCM2021/32/
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