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SUMMARY:Mario Garcia-Fernandez (Universidad Autónoma de Madrid)
DTSTART:20220526T150000Z
DTEND:20220526T160000Z
DTSTAMP:20260418T165023Z
UID:GTACoS/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GTACoS/5/">N
 on-Kähler Calabi-Yau geometry and pluriclosed flow</a>\nby Mario Garcia-F
 ernandez (Universidad Autónoma de Madrid) as part of Geometry & TACoS - S
 ession VIII : Complex Geometric Flows\n\n\nAbstract\nIn this talk I will o
 verview joint work with J. Jordan and J. Streets\, in arXiv:2106.13716\, a
 bout Hermitian\, pluriclosed metrics with vanishing Bismut-Ricci form. The
 se metrics give a natural extension of Calabi-Yau metrics to the setting o
 f complex\, non-Kähler manifolds\, and arise independently in mathematica
 l physics. We reinterpret this condition in terms of the Hermitian-Einstei
 n equation on an associated holomorphic Courant algebroid\, and thus refer
  to solutions as Bismut Hermitian-Einstein. This implies Mumford-Takemoto 
 slope stability obstructions\, and using these we exhibit infinitely many 
 topologically distinct complex manifolds in every dimension with vanishing
  first Chern class which do not admit Bismut Hermitian-Einstein metrics. T
 his reformulation also leads to a new description of pluriclosed flow\, as
  introduced by Streets and Tian\, implying new global existence results. I
 n particular\, on all complex non-Kähler surfaces of nonnegative Kodaira 
 dimension. On complex manifolds which admit Bismut-flat metrics we show gl
 obal existence and convergence of pluriclosed flow to a Bismut-flat metric
 .\n
LOCATION:https://researchseminars.org/talk/GTACoS/5/
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