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UID:fc04f44f774c7ab0a09b3d5d814a58d3
CATEGORIES:Mathematical Physics Seminar
CREATED:20220928T160316
SUMMARY:Random packings and liquid crystals
LOCATION:Hill Center Room 705
DESCRIPTION:Let T be a subset of R^d, such as a ball, a cube or a cylinder, and conside
 r all possibilities for packing translates of T, perhaps with its rotations
 , in some bounded domain in R^d. What does a typical packing of this sort l
 ook like? One mathematical formalization of this question is to fix the den
 sity of the packing and sample uniformly among all possible packings with t
 his density. Discrete versions of the question may be formulated on lattice
  graphs.\nThe question arises naturally in the sciences, where T may be tho
 ught of as a molecule and its packing is related to the spatial arrangement
  of molecules of a material under given conditions. In some cases, the mate
 rial forms a liquid crystal - states of matter which are, in a sense, betwe
 en liquids and crystals.\nI will review ideas from this topic, mentioning s
 ome of the predictions and the mathematical progress. Time permitting, I wi
 ll elaborate on a recent result, joint with Daniel Hadas, on the structure 
 of high-density packings of 2x2 squares with centers on the square lattice.
 \nThe talk is meant to be accessible to a general mathematical audience.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="margin-bottom: 10px; text-align: center;">Let T be a subset of R^
 d, such as a ball, a cube or a cylinder, and consider all possibilities for
  packing translates of T, perhaps with its rotations, in some bounded domai
 n in R^d. What does a typical packing of this sort look like? One mathemati
 cal formalization of this question is to fix the density of the packing and
  sample uniformly among all possible packings with this density. Discrete v
 ersions of the question may be formulated on lattice graphs.</p><p style="m
 argin-bottom: 10px; text-align: center;">The question arises naturally in t
 he sciences, where T may be thought of as a molecule and its packing is rel
 ated to the spatial arrangement of molecules of a material under given cond
 itions. In some cases, the material forms a liquid crystal - states of matt
 er which are, in a sense, between liquids and crystals.</p><p style="text-a
 lign: center; margin: 0in 0in 12pt;">I will review ideas from this topic, m
 entioning some of the predictions and the mathematical progress. Time permi
 tting, I will elaborate on a recent result, joint with Daniel Hadas, on the
  structure of high-density packings of 2x2 squares with centers on the squa
 re lattice.</p><p style="text-align: center; margin: 0in 0in 12pt;">The tal
 k is meant to be accessible to a general mathematical audience.</p>
CONTACT:Ron Peled - Tel Aviv University and Institute for Advanced Study
DTSTAMP:20260827T152221
DTSTART;TZID=America/New_York:20221006T120000
DTEND;TZID=America/New_York:20221006T130000
SEQUENCE:0
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