论文标题
探索Jean Bourgain的工具包
Exploring the toolkit of Jean Bourgain
论文作者
论文摘要
Gian-Carlo Rota曾经断言“每个数学家只有一些技巧”。乍一看，让·布尔加因（Jean Bourgain）作品中的宽广和独创性似乎是该格言的反例。但是，正如我们希望在本文中说明的那样，即使是波尔加恩也经常依靠一组核心工具，这些工具构成了许多不同数学领域中问题的基础。我们在此处讨论选定数量的这些工具，然后进行案例研究，以了解如何将Bourgain论文中的一个论点解释为其中几种工具的顺序应用。
Gian-Carlo Rota once asserted that "every mathematician only has a few tricks". The sheer breadth and ingenuity in the work of Jean Bourgain may at first glance appear to be a counterexample to this maxim. However, as we hope to illustrate in this article, even Bourgain relied frequently on a core set of tools, which formed the base from which problems in many disparate mathematical fields could then be attacked. We discuss a selected number of these tools here, and then perform a case study of how an argument in one of Bourgain's papers can be interpreted as a sequential application of several of these tools.
