标题： 罗伯特·朗兰兹的工作 显示英文标题

标题： The work of Robert Langlands

摘要： 这是一份关于罗伯特·朗兰兹工作的报告，是在他2018年获得阿贝尔奖之后撰写的。 它包括他在表示理论、自守形式、数论和算术几何等广泛领域的贡献。 我们努力传达他所有工作中贯穿始终的非凡连续性，这些工作源于数学的几个基本领域。 现在被称为朗兰兹纲领的内容代表了这些领域中一些最深奥部分的统一。 我们希望这份报告至少有一些部分能够被更广泛的数学界读者所理解。 其他部分不可避免地会更加困难。 然而，我们也可以希望这份报告以一种有助于更好地理解朗兰兹工作各个方面的方式呈现。 显示英文摘要

摘要： This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have tried to communicate the remarkable continuity that runs throughout all of his work, with its roots in several fundamental areas of mathematics. What is now known as the Langlands Program represents a unification of some of the deepest parts of these areas. We hope that at least some parts of the report will be accessible to a broader mathematical audience. Other parts will inevitably be more difficult. However, we can also hope that the report is presented in such a way as to lead to a better understanding of all sides of Langlands' work.