报告题目：Differential Galois groups, specialization and Matzat’s conjecture
时 间：2024年3月24日（星期日）9:00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、统计学与人工智能福建省高校重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师与研究生
报告摘要：Differential Galois theory is an extension of Galois theory, originally developed by Picard and Vessiot, and later expanded upon by Ritt and Kolchin. It generalizes the study of polynomial equations to linear differential equations. Over the past two decades, this theory has been further extended to encompass parametrized linear differential and difference equations, and they have found numerous applications in areas such as combinatorics and number theory. In this talk, we will begin with a brief introduction to differential Galois theory. Subsequently, we will present some recent developments in this field. When dealing with a linear differential equation with parameters, one may wonder how the algebraic properties of its solutions change as the parameters vary over some affine variety. Building upon Hrushovski’s work on computing differential Galois groups, we address this question. We will then apply our results to prove Matzat’s conjecture, which asserts that the absolute differential Galois group of a one-variable function field over an algebraically closed field of characteristic zero is a free proalgebraic group. This talk is based on collaborative work with Michael Wibmer from the University of Leeds, UK
报告人简介：中国科学院数学与系统科学研究院研究员、博士生导师，主要研究方向为：符号计算与微分差分伽罗华理论，特别是微分差分方程的符号求解、构造性线性微分（差分）方程伽罗华理论及其在特殊函数理论与组合数学等领域的应用。目前已在符号计算领域国际会议ISSAC，以及期刊Journal of Symbolic Computation， Advances in Applied Mathematics，Mathematics of Computation，Transactions of the AMS等发表论文20多篇。