Packing, coding, and ground states
Packing, coding, and ground states
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包装、编码和基态
DOI：
10.1090/pcms/023/02
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Henry Cohn
中科院分区：
文献类型：
--
作者：
Henry Cohn
这些是我2014年PCMI研究生暑期学校讲座的讲义。在这些讲座中，我们将从几个不同的角度研究材料的简单模型：几何（包装问题），信息论（纠错码）和物理（相互作用粒子系统的基态）。这些观点都揭示了一些相同的问题和现象，同时强调了不同的技术和联系。一个值得注意的现象是在某些特殊情况下发现的异常对称性，我们将研究何时以及为什么会发生。因此，讲座的总主题是有序与无序。在最佳几何结构中我们能期望看到多少对称性？
These are the lecture notes from my 2014 PCMI graduate summer school lectures. In these lectures, we'll study simple models of materials from several different perspectives: geometry (packing problems), information theory (error-correcting codes), and physics (ground states of interacting particle systems). These perspectives each shed light on some of the same problems and phenomena, while highlighting different techniques and connections. One noteworthy phenomenon is the exceptional symmetry that is found in certain special cases, and we'll examine when and why it occurs. The overall theme of the lectures is thus order vs. disorder. How much symmetry can we expect to see in optimal geometric structures?