发展方程的几何理论及应用专题讲习班

The geometric theory, describing the geometry of the flow, of differential equations was effectively initiated by Poincaré and Lyapunov. This theory concerns the existence of special solutions (equilibrium points, periodic solutions, almost-periodic solutions, etc.) or collections of solutions (invariant manifolds, attractor, limit set), and the stability or instability of these. Global questions are also considered (large time behavior starting from an “arbitrary” initial value). Since their work, there has been a large number of indepth studies on this topic and it is still one of the most heated topics in the world, which has attracted much attention of many mathematicians. The present special workshop focuses on the geometric theory of evolution equations (i.e., ordinary and partial differential equations with time variable t) with important application background and applications. The main purpose is to promote young teachers and graduate students in China's universities to study deeply the geometric theory of evolution equations, and to enhance the strength of scientific research and influence in this field. The workshop will invite several well-known professors to give systematic lectures (both basic courses and special courses), including semigroup of operators and evolution equation, partial differential equation, invariant manifold theory and monotone dynamical system, and organize an international conference. These professors are academically advanced, with research achievements recognized by domestic and foreign experts. Their courses will lead young teachers and graduate students to the international frontiers of the research of geometric theory of evolution equations.

著名数学家Poincaré和Lyapunov开创了微分方程几何理论(描述流的几何)这一研究分支。该理论涉及特解(平衡点、周期解、几乎周期解等)或解族(不变流形、吸引子、极限集)的存在性、稳定性和不稳定性，也考虑一些全局问题(任意初值解的大时间行为)。自这些工作以来，已有众多文献对这类问题进行深入研究，目前仍是国际上一个热门课题，引起了广泛关注。本专题讲习班关注发展方程即包含时间变量且具有重要应用背景的常微分方程和偏微分方程的几何理论及应用。主要目的是推动国内高校青年教师和研究生深入学习发展方程的几何理论，提升在该领域的科研实力和影响力。讲习班将邀请国内几位知名专家进行系统授课(既有基础课又有专题课)，并举办国际会议。授课内容有算子半群与发展方程、偏微分方程基础、不变流形理论和单调动力系统理论。这些专家在本研究领域有很高学术造诣，他们的授课将引领青年教师和研究生在本研究领域走向国际前沿。

该项目是一个致力于发展方程的几何理论及应用专题讲习班。由于受疫情影响，我们采用线上进行。本次讲习班邀请了4名微分方程领域的知名专家开展了为期10天的2门基础课，2门专业课的授课，又邀请了来自中国、美国、加拿大等国内外14名该领域的专家举办了2天的国际研讨会。来自南京大学、中国科学技术大学、东南大学、大连理工大学、华中师范大学、西安交通大学、四川大学、兰州大学、华中科技大学、北京工业大学、中国地质大学、中国矿业大学等80多所院校的600余名硕士、博士、博士后及教师参加了学习，本项目搭建了一个培养青年人才、促进学术交流、提升数学创新应用能力的高质量学习平台，使得国内青年教师及研究生关于算子半群、偏微分方程、不变流形理论和单调动力系统的理论基础得到了夯实，从而引领他们走向发展方程几何理论研究的国际前沿。