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SUMMARY:Francisco Nascimento (Instituto Superior Técnico\, Universidade d
 e Lisboa)
DTSTART:20241203T160000Z
DTEND:20241203T170000Z
DTSTAMP:20260423T022745Z
UID:Geolis/158
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/158/"
 >Kinematic formulas in convex geometry</a>\nby Francisco Nascimento (Insti
 tuto Superior Técnico\, Universidade de Lisboa) as part of Geometria em L
 isboa (IST)\n\n\nAbstract\nWe present a systematic study of kinematic form
 ulas in convex geometry. We first give a classical presentation of kinemat
 ic formulas for integration with respect to the rotation group $SO(n)$\, w
 here Steiner's Formula\, the intrinsic volumes and Hadwiger's Characteriza
 tion Theorem play a crucial role. Then we will show a new extension to int
 egration along the general linear group $GL(n)$. Using the bijection of ma
 trix polar decomposition and a Gaussian measure to integrate along positiv
 e definite matrices\, a new formula is obtained\, for which the classical 
 $SO(n)$ formula is a particular case. We also reference the unitary group 
 $U(n)$ case and its corresponding extension to the symplectic group $Sp(2n
 \,\\mathbb{R})$.\n
LOCATION:https://researchseminars.org/talk/Geolis/158/
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