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VERSION:2.0
PRODID:-//University of Liverpool Computer Science Seminar System//v2//EN
BEGIN:VEVENT
DTSTAMP:20260921T211523Z
UID:Seminar-MIF-1374@lxserverM.csc.liv.ac.uk
ORGANIZER:CN=Othon Michail:MAILTO:Othon.Michail@liverpool.ac.uk
DTSTART:20211112T140000
DTEND:20211112T150000
SUMMARY:MIF Series
DESCRIPTION:Vitaly Kurlin: Continuous metrics on isometry classes of 2-dimensional lattices.\n\nA periodic lattice is an infinite set of all integer linear combinations of basis vectors in a Euclidean space. A natural equivalence on lattices is rigid motion (a composition of translations and rotations) or isometry (also including reflections). All 2-dimensional lattices can be parametrised by three real parameters, but there was no easy metric on isometry classes of lattices, which is also continuous under basis perturbations. Using a recent parametrisation of 2-dimensional lattices by root forms, we introduce metrics that are invariant up to isometry or up to rigid motion, which preserves orientation. The latter case also quantifies chirality by measuring a distance from a chiral lattice to its closest mirror-symmetric neighbour. The talk is based on the updated dimension 2 paper joint with Matt Bright and Andy Cooper.\n\nhttps://www.csc.liv.ac.uk/research/seminars/abstract.php?id=1374
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