BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Markus Kiderlen (Aarhus University) DTSTART:20250226T140000Z DTEND:20250226T160000Z DTSTAMP:20260423T010747Z UID:GPL/44 DESCRIPTION:Title: Cro fton-type Formulae in Rotational Integral Geometry\nby Markus Kiderlen (Aarhus University) as part of Geometry and Physics @ Lisbon\n\nLecture h eld in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThe purpose of th is talk is to give an introduction to rotational integral geometry and exe mplify a number of its core results and their applications. Integral geome try\, introduced by Blaschke in the 1930s\, is the theory of invariant me asures on geometric spaces (often Grassmannians) and its application to de termine geometric probabilities.\n\nWe will start by recalling the kinemat ic Crofton formula\, which allows us to retrieve certain geometric charact eristics (such as volume\, surface area and other intrinsic volumes) of a compact convex set $K$ in $\\mathbb R^n$ from intersections with invariant ly integrated $k$-dimensional affine subspaces\, where $k=0\,\\ldots\,n-1$ is fixed.\n\nMotivated by applications from biology\, we suggest a number of variants of Crofton's formula\, where the intersecting affine spaces a re constrained to contain the origin -- and hence are just linear subspace s -- or even all contain a fixed lower-dimensional axis. Corresponding rot ational Crofton formulae will be established and explained. We also show that the set of these formulae is complete in that they retrieve all possi ble intrinsic volumes of $K$. Proofs rely on old and new Blaschke-Petkants chin theorems\, which we also will outline.\n\nJoint work with Emil Dare a nd Eva B. Vedel Jensen.\n LOCATION:https://researchseminars.org/talk/GPL/44/ END:VEVENT END:VCALENDAR