Mathematical Sciences: Moduli Problems and Iterated Loop Spaces in Mathematical Physics

查尔斯·博耶将继续他对数学物理中出现的模问题的研究。这是目前数学中最活跃的领域之一，并已被证明对数学物理、拓扑和几何具有深远的影响。Boyer的许多工作的动机是认识到数学和数学物理中的许多模问题与迭代循环空间的同伦理论密切相关。正是这种观察揭示了模空间的拓扑和底层四维流形的微分拓扑之间的关系。Boyer的工作有望进一步阐明这种关系。它也有希望揭示代数拓扑和几何非线性偏微分方程之间的联系的更深层次的理解。

Charles Boyer will continue his research into moduli problems which arise in mathematical physics. This is currently one of the most active areas of mathematics and has been shown to have profound consequences in mathematical physics, topology and geometry. The motivation for much of Boyer's work is the realization that many moduli problems in mathematics and mathematical physics are intimately related to the homotopy theory of iterated loop spaces. It is this observation that reveals the relationship between the topology of the moduli spaces and the differential topology of the underlying four dimensional manifold. Boyer's work is expected to shed further light on this relationship. It also holds promise of revealing deeper understanding of connections between algebraic topology and geometric non-linear partial differential equations.