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DTSTAMP:20260605T131255Z
DESCRIPTION:Title: Nash and Whitney problems in convex valuation theory\n\n
 Abstract: A (convex\, smooth) valuation is a finitely additive measure on 
 convex bodies\, satisfying a smoothness condition\; many interesting objec
 ts in convex and differential geometry are in fact valuations.\n\nAssume t
 hat a collection of valuations is given on a family S of subspaces of R^n 
 . Are they the restrictions of a single valuation? Clearly\, compatibility
  of the given data on intersections is a necessary condition. Is it suffic
 ient?\n\nWe will discuss several geometrically distinct instances of this 
 problem\, whence it acquires distinct flavors.\n\nWhen S is the whole k-gr
 assmannian\, and the valuations j-homogeneous\, we will see that the condi
 tion is sufficient\, provided k-j>1. This can be seen as a dimensional loc
 alization of the transition from densities to valuations.\n\nIn another se
 tting where S consists of pairwise non-intersecting subspaces\, we again e
 stablish a positive answer. As a corollary\, we will deduce a Nash embeddi
 ng theorem for smooth valuations on manifolds.\n\nFinally\, we will consid
 er the setting of finite generic families of subspaces\, giving rise to a 
 surprising extension phenomenon.\n\nBased on a joint work with Georg Hofst
 aetter.\n\nCRM\, Université de Montréal\, Pavillon André-Aisenstadt\, room
  5340\, and by Zoom (see link below)\n\nJoin Zoom Meeting\n\nhttps://us06w
 eb.zoom.us/j/83180453914?pwd=RQnoWH7aQqXAxldXZsqdafFCmh7dBC.1\n\nMeeting I
 D: 831 8045 3914\n\nPasscode: 719821\n
DTSTART:20231124T190000Z
DTEND:20231124T200000Z
SUMMARY:Dmitry Faifman (Tel Aviv University)
URL:https://www.mcgill.ca/mathstat/channels/event/dmitry-faifman-tel-aviv-u
 niversity-352834
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