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BEGIN:VEVENT
DTSTAMP:20230331T082622Z
DTSTART:20230426T140000Z
DTEND:20230426T150000Z
SUMMARY:SQUIDS Seminar: Vitaliy Kurlin - Geometric Data Science: old chal
lenges and new solutions
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DESCRIPTION:Join us for this research seminar\, part of the SQUIDS (Stati
stics\, quantification of uncertainty\, inverse problems and data scienc
e) seminar series.\n\nAbstract: Geometric Data Science (GDS) studies mod
uli spaces of data objects up to important equivalences. The key example
is a finite or periodic set of unlabelled points up to rigid motion or
isometry preserving inter-point distances. The best known result in the
finite case was the SSS theorem saying that triangles are completely cla
ssified by a triple of their sides. There was no similar continuous inva
riant even for 4 points in the plane partially due to a 4-parameter fami
ly of 4-point clouds that have the same 6 pairwise distances. One major
result is a complete and continuous invariant for clouds of m unlabeled
points in any Euclidean space\, to appear in CVPR 2023.\n\nThe classific
ation problem for periodic point sets\, which model all crystalline mate
rials\, is substantially harder and cannot be reduced to a finite cloud
because the smallest pattern (a unit cell) of a periodic crystal is disc
ontinuous under tiny (or thermal) vibrations of atoms. This ambiguity w
as resolved by generically complete and continuous Pointwise Distance Di
stributions (PDD). The near-linear time algorithm for PDD invariants was
tested via more than 200 billion pairwise comparisons of all 660K+ per
iodic crystals in the world's largest collection of real materials: the
Cambridge Structural Database. This experiment took only two days on a m
odest desktop and detected five pairs of geometric duplicates. In each p
air\, the crystals are truly isometric to each other but one atom is rep
laced with a different atom type\, which seems physically impossible wit
hout perturbing geometry. Five journals are investigating the integrity
of the underlying articles.\n\nThe more important conclusion is the Crys
tal Isometry Principle meaning that all real periodic crystals have uniq
ue geographic-style locations in a common continuous Crystal Isometry Sp
ace (CRISP)\, published in NeurIPS 2022. Hence complete invariants form
a DNA-style code or materials genome that parametrises a continuous map
of CRISP including all known and not yet discovered crystals. All releva
nt papers are co-authored with many Liverpool colleagues\, see http://ku
rlin.org/research-papers.php#Geometric-Data-Science.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 2\, Alan Turing Building\, Manchester
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