【系综合学术报告】第38期

题目：Uniformly rotating vortex patches with 90-degree corners for the 2-D incompressible Euler equation

报告人：黄得（北京大学数学学院）

时间：2026年10月15日（星期四）14:00-15:00

地点：双清综合楼304教室

摘要：We will discuss our proof of, for the first time, the existence of uniformly rotating vortex patches with 90-degree corners for the 2-D incompressible Euler equation. Our construction builds upon a novel free-boundary fixed-point approach that pins down the 90-degree-corner condition. This is also the first example where a steady vortex patch solution has lasting isolated 90-degree corners. This is based on a joint work with Jiajun Tong and Xiaopeng Zheng.

【系综合学术报告】第39期

题目：Controlled geometric flows of maps

报告人：向圣权（北京大学数学学院）

时间：2026年10月15日（星期四）15:00-16:00

地点：双清综合楼304教室

摘要： In this talk, we discuss controlled geometric flows of maps, motivated by the heat flow and wave maps, in which control is incorporated into geometric evolution equations. Unlike classical control problems in flat PDE settings, the geometry and topology of the target manifold directly influence both the dynamics and its controllability, leading to phenomena that do not arise in Euclidean models.  Based on joint work with Jean-Michel Coron and Joachim Krieger.