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UID:c16388cc8e10200bfcb02755a6899108
CATEGORIES:Mathematical Physics Seminar
CREATED:20230118T093404
SUMMARY:Random packings and liquid crystals
LOCATION:Zoom
DESCRIPTION:<p style="text-align: left;">Abstract: Let T be a subset of R^d, such as a 
 ball, a cube or a cylinder, and consider all possibilities for packing tran
 slates of T, perhaps with its rotations, in some bounded domain in R^d. Wha
 t does a typical packing of this sort look like? One mathematical formaliza
 tion of this question is to fix the density of the packing and sample unifo
 rmly among all possible packings with this density. Discrete versions of th
 e question may be formulated on lattice graphs. The question arises natural
 ly in the sciences, where T may be thought of as a molecule and its packing
  is related to the spatial arrangement of molecules of a material under giv
 en conditions. In some cases, the material forms a liquid crystal - states 
 of matter which are, in a sense, between liquids and crystals. I will give 
 a gentle review of ideas from this topic, mentioning some of the prediction
 s and the mathematical progress. I will then elaborate on a recent result, 
 joint with Daniel Hadas, on the structure of high-density packings of 2x2 s
 quares with centers on the square lattice.</p>
CONTACT:Ron Peled – Tel Aviv University
DTSTAMP:20260828T114633
DTSTART;TZID=America/New_York:20230125T104500
DTEND;TZID=America/New_York:20230125T114500
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