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利玛窦曲率界综合理论——当信息论、优化、几何和梯度流相遇时

Synthetic theory of Ricci curvature - when information theory, optimization, geometry and gradient flows meet
课程网址: http://videolectures.net/colt2015_villani_ricci_curvature/  
主讲教师: Cédric Villani
开课单位: 亨利·庞加莱学院
开课时间: 2015-08-20
课程语种: 英语
中文简介:
这是一个数学理论的故事,它诞生于几个领域的相遇。这些领域是:黎曼几何、梯度流、信息和最优传输;他们的相遇发生在大约15年前。这种相互作用的一个主要结果是利玛窦曲率界的综合理论,该理论于2005年左右正式化,经过十年的快速持续增长,现在似乎已经成熟。由于该理论仍处于快速发展中,即使对专家来说,也很难准确追踪其进展。
课程简介: This is the story of a mathematical theory which was born from the encounter of several fields. Those fields were: Riemannian geometry, gradient flows, information, and optimal transport; and their encounter took place about 15 years ago. A major result of the interaction was the synthetic theory of Ricci curvature bounds, which was formalized around 2005 and now seems to be reaching maturity, after ten years of fast, sustained growth. As the theory is still in rapid evolution, it is often difficult, even for experts, to trace its progress accurately.
关 键 词: 数学理论; 黎曼几何; 综合理论
课程来源: 视频讲座网
数据采集: 2023-06-08:chenxin01
最后编审: 2023-06-08:chenxin01
阅读次数: 16