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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20220130T145745Z
DTSTART:20220208T150000Z
DTEND:20220208T160000Z
SUMMARY:Ioannis Tsokanos (Manchester) - Visibility properties in Spirals
and Forests
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}z142-kz1e0f
sk-g3w5hj
DESCRIPTION:Abstract : A spiral in the d-dimensional Euclidean space is a
point set of the form S(U) = { k^{1/d+1} * u_k }_{k}\, where U = (u_k)
_{k} is a sequence in the (d-1)-dimensional unit sphere. \nA Peres-type
forest F(a) is the planar point set containing all the points of the f
orm (k \, l + a_k) or (l + a_k \, k) with k\,l integers and where a =
(a_k)_{k} is a sequence in the unit torus.\n\nThe talk is concerned with
the study of the distributional properties of spirals and Peres-type fo
rests in the Euclidean space. To characterize such distributional proper
ties\, we employ notions from discrete geometry and visibility concepts.
For instance\, a Delone set (in discrete geometry) is a point set whic
h is simultaneously uniform discrete (there exists a positive infimum di
stance between any two points of the set) and relatively dense (the dist
ance of the set from any point of the space is upper bounded). Also\, a
point set Y has an empty set of visible points if\, for any point x in \
\R^{d} and any direction v in the (d-1)-dimensional sphere\, the distanc
e of Y from the half-line { x + tv}_{t > 0} is zero.\n\nBoth structures
under consideration (spirals and Peres-type forests) are defined with t
he help of a sequence whose terms are chosen in a proper space (the sphe
re and the torus\, respectively). This talk has two goals: (1) to provid
e necessary and sufficient conditions on a spherical (resp. on a toral)
sequence for the spiral (resp. the Peres' forest) which it generates to
satisfy the aforementioned visibility concepts and (2) to exploit number
theoretical tools from the theories of distribution of sequences modulo
one and Diophantine approximation to guarantee the existence of spiral
structures (resp. Peres' forests) satisfying the properties of being Del
one or having an empty set of visible points. \n\n\n\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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