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SUMMARY:Canonical barriers on convex cones
DTSTART:20161207T134000Z
DTEND:20161207T143000Z
DTSTAMP:20241014T232200Z
UID:indico-event-1749@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Roland HILDEBRAND (Université Grenoble-Alpes)\n\nTh
e Calabi theorem states that for every regular convex cone K in R^n\, the
Monge-Ampère equation log det F” = 2F/n has a unique convex solution on
the interior of K which tends to +infty on the boundary of K. It turns ou
t that this solution is self-concordant and logarithmically homogeneous\,
and thus is a barrier which can be used for conic optimization. We conside
r different aspects of this barrier:\n\n\n affine spheres as level surf
aces\n metrization of the interior of K by the Hessian metric F”\n
primal-dual symmetry\n interpretation as a minimal Lagrangian submanif
old in a certain para-Kähler space form\n complex-analytic structure o
n 3-dimensional cones.\n\n\nhttps://indico.math.cnrs.fr/event/1749/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/1749/
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