Mathematical Sciences: Descriptive Set Theory

这个项目涉及描述性集合理论的各个方面以及它与分析的关系。这些包括(i)研究Borel等价关系的结构，既在一般的描述性集合理论背景下，也与遍历理论中出现的特定情况有关，例如，由群作用轨道引起的等价关系；(2)调和分析和算子代数理论中的可定义性和描述性分类问题。

This project deals with aspects of descriptive set theory and its relationship with analysis. These include (i) the study of the structure of Borel equivalence relations, both in a general descriptive set theoretic context, as well as in connection with specific situations arising in ergodic theory, as, for example, with equivalence relations induced by orbits of group actions, and (ii) definability and descriptive classification problems in harmonic analysis and the theory of operator algebras.