Moduli spaces of meromorphic connections and the Fourier transform

Stokes现象出现在具有不规则奇点的复微分方程理论中，并且众所周知，微分系统由其Stokes数据确定。傅里叶-拉普拉斯变换是数学和物理学中的一个重要的积分变换，斯托克斯数据在这种变换下的行为是一个活跃的研究领域。在这个项目中，我们的目标是更好地理解几何的傅里叶-拉普拉斯变换相结合的两个问题，一直在文献中的极大兴趣：一方面，显式计算的傅里叶-拉普拉斯变换的斯托克斯数据;另一方面，亚纯微分方程的模空间的建设。具体地说，我们首先要执行明确的计算的傅里叶-拉普拉斯行动斯托克斯数据，利用最近的发展，这给我们提供了强大的工具，这样的考虑：理论增强ind-sheaves的D 'Agnolo-Kashiwara。其次，我们将使用这些结果来描述由傅里叶-拉普拉斯变换诱导的模空间上的Stokes数据的同构，并研究它们的行为相对于这些空间上的几何结构。

Stokes phenomena occur in the theory of complex differential equations with irregular singularities, and it is well-known that a differential system is determined by its Stokes data. The Fourier-Laplace transform is a prominent integral transform in all of mathematics and physics, and the behaviour of Stokes data under this transformation is an active field of research. In this project, we aim at understanding better the geometry of the Fourier-Laplace transformation by combining two questions that have been of great interest in the literature: On the one hand, the explicit computation of Fourier-Laplace transforms of Stokes data; on the other hand the construction of moduli spaces of meromorphic differential equations. Concretely, we first want to perform explicit computations of the Fourier-Laplace action on Stokes data, making use of recent developments which give us powerful tools for such considerations: the theory of enhanced ind-sheaves of D’Agnolo-Kashiwara. Secondly, we will use these results to describe the isomorphisms induced by Fourier-Laplace transform on moduli spaces of Stokes data and study their behaviour with respect to geometric structures on these spaces.