Scientists and philosophers had speculated about the nature of space for at least 2500 years. Modern geometry started with the ideas of Gauss and Riemann.
They identified curvature as the fundamental concept for describing geometric spaces. This made fundamental mathematical advances possible and also enabled Einstein's theory of general relativity. Riemannian geometry is also the language of modern quantum field theory. At the same time, geometry has become ever more abstract, for instance proposing abstract versions of curvature, for example useful for data analysis.
I will explain the mathematical concepts, like curvature, connections, Laplace type operators and geometrically constructed action functionals.
嘉宾介绍
Jürgen Jost
德国国家科学院院士演讲主题：
Professor Jürgen Jost is a world-renowned mathematician who has made fundamental contributions to numerous fields of geometric analysis, including the theory of harmonic maps and its applications in geometry and mathematical physics, minimal submanifolds, and discrete geometry. He has published more than 500 academic papers and authored over 20 monographs, with his work cited more than 15,000 times. He received the Leibniz Prize—the highest research award in Germany—in 1993, the European Research Council Advanced Grant in 2010, the Teubner Foundation Science Prize in 2018, and the Shanghai International Science and Technology Cooperation Award in 2024.