2024华罗庚青年数学论坛（分析及其相关方向）
会议日程
时间：2024年7月6日9:00-16:00
地点：数学院南楼N818
| 时间 | 事项 |
| 08:40-09:00 | 背景介绍 |
| 09:00-09:50 | 报告1 杨洋 |
| 10:00-10:30 | 休息 |
| 10:30-11:20 | 报告2 沈大卫 |
| 下午 | |
| 14:00-14:50 | 报告3 江孚帅 |
| 15:00-15:30 | 休息 |
| 15:30-16:20 | 报告4 甘盛文 |
报告题目及摘要
报告1 杨洋 Johns Hopkins
Title：The anisotropic Bernstein problem (各向异性Berntein问题)
Abstract：The Bernstein problem asks whether entire minimal graphs in R^{n+1} are necessarily hyperplanes. It is known through spectacular work of Bernstein, Fleming, De Giorgi, Almgren, Simons, and Bombieri-De Giorgi-Giusti that the answer is positive if and only if n < 8. The anisotropic Bernstein problem asks the same question about minimizers of parametric elliptic functionals, which are natural generalizations of the area functional that both arise in many applications and offer important technical challenges. We will discuss the recent solution of this problem (the answer is positive if and only if n < 4). This is joint work with C. Mooney.
报告2 沈大卫 Laboratoire Jacques-Louis Lions, Sorbonne Université,
Title: Global stability of Minkowski spacetime with minimal decay
Abstract: The global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou-Klainerman in 1993. In 2007, Bieri has extended the result of Christodoulou-Klainerman under lower decay and regularity assumptions on the initial data. In this talk, I will introduce my recent work, which extends the result of Bieri to minimal decay assumptions. If time permits, I will discuss another recent work, which prove that the exterior stability of Minkowski holds with decay which is borderline.
报告3 江孚帅 University of Maryland
Title: Smooth selection of convex sets
Abstract: I plan to describe a unified approach to studying three seemingly unrelated problems. The first problem concerns extending a function from partial data (interpolation), the second problem concerns smooth selections of set-valued mappings (control theory), and the third problem concerns solving an underdetermined linear system of inequalities (semialgebraic geometry). The process is in terms of the Glaeser refinement of a suitable "bundle", used by C. Fefferman in his full solution to the Whitney extension problem. This is joint work with Kevin Luli (UC Davis) and Kevin O'Neill (Yale University).
报告4 甘盛文 University of Wisconsin-Madison
Title: An estimate for Hormander-type oscillatory integral operator with certain nondegeneracy condition
Abstract：这次报告中，我将介绍Hormander型振荡积分算子。对于一般的Hormander型振荡积分算子，最好的L^p估计的指标是Stein-Tomas指标。 我们研究满足某种非退化条件的振荡积分算子，并证明再此条件下L^p估计的指标p能被改进。
