Mathematical Sciences: The Foundations of Mathematics

辛普森将在二阶算术的子系统的背景下继续他对普通数学的公理研究。研究的内容包括：(1)希尔伯特程序和泛函分析；(2)基于多项式时间可计算性的希尔伯特程序的变体；(3)可数代数和可数组合学背景下的逆数学。这样的研究阐明了可计算性和其他基础性问题的理论极限。

Simpson will continue his axiomatic studies of ordinary mathematics in the context of subsystems of second order arithmetic. Aspects of the research include: (1) Hilbert's program and functional analysis; (2) a variant of Hilbert's program based on polynomial time computability; (3) reverse mathematics in the context of countable algebra and countable combinatorics. Such studies illuminate the theoretical limits of computability and other foundational matters.