报告题目: Polytope Numbers
报告人：Hyun Kwang Kim 教授  Pohang University of Science and Technology
时间: 10月18日（周日）下午3:30-4:30
地点：管研楼1518
摘要: A classical theorem of Lagrange, known as the sum of four squares,
states that every positive integer can be written as the sum of four
squares. The theme of this lecture is various generalizations of
Lagrange's sum of four squares.

  In the first, we introduce two classical generalizations of sum of four
squares, namely Cauchy's polygonal number theorem and Waring's problem.
Next we introduce `polytope numbers' which, on one hand, can be viewed
as a higher dimensional generalization of Cauchy's polygonal numbers,
and on the other hand, can be viewed as horizontal generalization of
$k^{th}$ power in Waring's problem.

  Finally we discuss basic properties of polytope numbers and our recent
results on asymptotic order of the set of polytope numbers of a convex
polytope.

报告人简介: HyunKwang Kim教授任职于韩国浦项理工大学（Postech), 曾任数学
系主任，为国际著名组合数论和编码专家。

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