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SUMMARY:Integral geometry of flag area measures
DTSTART:20191028T161500
DTEND:20191028T173000
DTSTAMP:20260510T040511Z
UID:6e531a72567195563b8d676dd746e726adeb519056dbc6372a59e954
CATEGORIES:Conferences - Seminars
DESCRIPTION:Judith Abardia (Frankfurt) \nKinematic formulas are one of the
  main object of study in integral geometry. They express the average of a 
 geometric functional over a group acting on the space of convex bodies\, i
 n terms of some other geometric functionals. In the classical kinematic fo
 rmulas\, the intrinsic volumes are considered and the integral can be expr
 essed in terms of all intrinsic volumes only.\n\nIn this talk\, I shall pr
 esent a joint work with Andreas Bernig\, where we obtain additive kinemati
 c formulas for smooth flag area measures. A flag area measure on a Euclide
 an vector space is a continuous and translation-invariant valuation (addit
 ive functional from the space of convex bodies) with values in the space o
 f signed measures on a fixed flag manifold.\n\nAfter stating the existence
  of such additive kinematic formulas\, I will consider the particular case
  of the flag manifold consisting of a unit vector and a linear subspace of
  fixed dimension which contains the unit vector. We will first give a basi
 s of these flag area measures and interpret geometrically its elements. Th
 e kinematic formulas will be obtained after moving to the dual space of fl
 ag area measure and studying its structure of algebra.
LOCATION:MA B1 524
STATUS:CONFIRMED
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