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SUMMARY:Timothy Magee (Birmingham)
DTSTART:20201203T133000Z
DTEND:20201203T143000Z
DTSTAMP:20260423T024807Z
UID:notts_ag/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/notts_ag/39/
 ">Convexity in tropical spaces and compactifications of cluster varieties<
 /a>\nby Timothy Magee (Birmingham) as part of Online Nottingham algebraic 
 geometry seminar\n\n\nAbstract\nCluster varieties are a relatively new\, b
 roadly interesting class of geometric objects that generalize toric variet
 ies. Convexity is a key notion in toric geometry. For instance\, projectiv
 e toric varieties are defined by convex lattice polytopes. In this talk\, 
 I'll explain how convexity generalizes to the cluster world\, where "polyt
 opes" live in a tropical space rather than a vector space and "convex poly
 topes" define projective compactifications of cluster varieties. Time perm
 itting\, I'll conclude with two exciting applications of this more general
  notion of convexity: 1) an intrinsic version of Newton-Okounkov bodies an
 d 2) a possible cluster version of a classic toric mirror symmetry constru
 ction due to Batyrev.  Based on joint work with Man-Wai Cheung and Alfredo
  Nájera Chávez.\n
LOCATION:https://researchseminars.org/talk/notts_ag/39/
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