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DTSTAMP:20261017T015656Z
LAST-MODIFIED:20200212T175040Z
DTSTART:20200212T193000Z
DTEND:20200212T210000Z
UID:event2299@bu.edu
URL:http://physics.bu.edu/internal/events/show/2299
SUMMARY:A macro-meso-microscopic view of disk packing 
DESCRIPTION:Featuring James Propp\, UMass Lowell\nHosted by: Julian Ingham\
	n\nPart of the Condensed Matter Theory Seminar Series.\n\nEveryone knows he
	xagonal close-packings are the most efficient way to pack unit disks in R^2
	. But what do we mean by the definite article "the" in the previous sentenc
	e? Are hexagonal close-packings the only optimal packings? If we measure op
	timality by density\, the answer is\, No. In fact\, there are far too many 
	density-optimal packings to classify in any meaningful way. This suggests t
	hat density is too coarse a notion to capture everything that we mean (or s
	hould mean!) by "efficient".\n\nTo study efficiency\, we study deficiency\,
	 and seek ways to quantify defects in a regular packing. An obstacle here i
	s that common kinds of defects inhabit disparate scales (e.g.\, point defec
	ts are infinitesimal compared to line defects\, which in turn are infinites
	imal compared to the bulk). This suggests we turn to extensions of the real
	 numbers that include infinitesimal elements (or rather\, as turns out to b
	e more helpful\, infinite elements).\n\nWe use a regularization trick to ma
	ke sense of these ideas. This enables us to sharpen our notion of optimal p
	acking so that the optimal disk-packings are provably the hexagonal close-p
	ackings and no others. Unfortunately\, the notion of deficiency covered by 
	this theorem is not the most natural one\, nor is it the one most directly 
	applicable to higher-dimensional problems. This is very much work-in-progre
	ss and I'm hoping others can help!
LOCATION:SCI 328\, 590 Commonwealth Avenue\, 02215
STATUS:CONFIRMED
CLASS:PUBLIC
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