Combinatorial geometry in discrete math and harmonic analysis

在过去的25年里，谐波分析和组合学越来越紧密地联系在一起。Jean Bourgain, Nets Katz, Wilhelm Schlag, Terence Tao， Tom Wolff和其他许多人已经将谐波分析问题离散化，并将其重新定义为组合几何中的问题。在相反的方向上，最近和不断发展的离散分析领域使用分析中的工具和思想来解决传统上属于组合学范围的问题。从广义上讲，我的工作是在几何组合和经典调和分析的交叉点，并在几个相关的方向蔓延。

Over the past 25 years, harmonic analysis and combinatorics have become increasingly entwined. Jean Bourgain, Nets Katz, Wilhelm Schlag, Terence Tao, Tom Wolff, and many others have discretized harmonic analysis problems and recast them as questions in combinatorial geometry. In the opposite direction, the recent and growing field of discrete analysis uses tools and ideas from analysis to attack problems that have traditionally been the purview of combinatorics. Broadly speaking, my work lies at the intersection of geometric combinatorics and classical harmonic analysis, and sprawls in several related directions.