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SUMMARY:On the geometry of strong $G_2$-structures with torsion
DTSTART:20250620T091500Z
DTEND:20250620T101500Z
DTSTAMP:20260610T234700Z
UID:indico-event-14349@indico.math.cnrs.fr
DESCRIPTION:Speakers: Udhav Fowdar (Université de Turin)\n\nA strong geom
 etry with torsion corresponds to a Riemannian manifold carrying a metric c
 onnection with closed skew-symmetric torsion. When this connection has red
 uced holonomy group $H$\, then we say that the underlying $H$-structure is
  strong.This notion of strong geometry with torsion has been predominantly
  studied in the context of Hermitian geometry\, i.e. when $H=U(n)$\; such 
 manifolds are known as strong Kahler with torsion (SKT) or pluriclosed man
 ifolds. In this talk\, I will discuss the corresponding notion in the cont
 ext of $G_2$ geometry. I will explain the analogy with (almost) SKT manifo
 lds and give some new results characterising Ricci-flat strong $G_2$ manif
 olds with torsion. I will also explain how the same ideas can be applied t
 o $6$-manifolds with suitable $SU(3)$-structures. In the spirit of making 
 analogies with Hermitian geometry\, I will also discuss a $G_2$ version of
  Gauduchon connections and the pluriclosed flow. This is based on joint wo
 rks with Anna Fino.\n\nhttps://indico.math.cnrs.fr/event/14349/
LOCATION:112 (ICJ)
URL:https://indico.math.cnrs.fr/event/14349/
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