调和分析短期课程
课题名称 Selected Topics on Poincaré Inequalities
报告人 Feng Dai (University of Alberta)
课程介绍
This lecture series explores both classical concepts and advanced extensions of Poincaré inequalities. The course begins with foundational principles in Euclidean spaces before expanding into general measure metric spaces. A major focus of the series will be analyzing Poincaré inequalities without the doubling condition of the underlying measures.
Core Topics
• Classical Foundations: An introduction to Poincaré inequalities in Euclidean spaces, exploring various versions, extensions, and typical applications.
• General Measure Metric Spaces: Advanced extensions of Poincaré inequalities across different metric spaces.
• High-Dimensional Probability: The intersection of Poincaré inequalities with semigroups and concentration inequalities.
Course Structure & Methodology
The series is broken down into several two-hour sessions. In each lecture, the instructor will introduce a specific topic, summarize the main results, outline potential proofs, and provide curated references for further exploration.
Beyond the structured lectures, dedicated time will be set aside for collaborative group discussions and recommended reading assignments.
课程时间 每节课时长2小时 (7月 6日首节课时间为20:00–22:00; 后续课程具体时间安排将于首节课后确定并通知). 日期见以下:
• 7月: 6, 13, 20, 30
• 8月: 3, 7, 10, 14, 17, 20
课程地点 后主楼1124
