Abstract

The curvature tensor captures the essential geometry of a Riemannian manifold. Curvaturebounds have important geometric, analvtical and topoloaical conseauences, in tum. these can beused for axiomatic characterizations of curvature bounds and extended to general metric spaces.Problems of modemn data analysis lead to a new perspective on curvature that will bedeveloped in this lecture, and surprising links to other mathematical concepts will emerge.

Speaker

From 1984-1996, Jurgen Jost was Professor of Mathematics at the Ruhr University inBochum. In 1996, he became a founding director of the Max Planck Institute for Mathematics inthe Sciences, Leipzig, Gemany. He is also an Honorary Professor at the University of Leipzigand an Extemal Professor of the Santa Fe Institute for the Sciences of Complexity in the USA. Heis a member of the Academy of Sciences Leopoldina (the National Academy of Gemmany), theAcademy of Sciences and Literature, Mainz, and the Saxonian Academy of Sciences and he wasthe founding and managing editor of the Joumal of the European Mathematical Society, one of thetop mathematical joummals in the world.Professor Jost is a world-renowned mathematician, who has published about 500 scientificarticles, and more than 20 monographs and textbooks, and his works have been cited morethan 20000 times. He has supervised more than 60 PhD students. Professor Jost has mademany important contrilbutions to several areas of mathematics, like the geometry and analysis onmanifolds, minimal submanifolds, harmonic maps and their applications in geometry, geometry olmetric spaces, Kaehler geometry, graph theory etc. which have become classical works in thosefields. As early as 1986, he was invited speaker at the Intemational Congress of Mathematiciansin Berkeley. In 1993, Professor Jost received the Gottfried Wilhelm Leibniz Prize. the mosidistinguished research award in Gemmany. in 2023, he received an honorary doctorate from theVietnam Academy of Science and Technology.

Professor dost is not only a leading expert in the field of geometric analysis, but also hasmade important contributions to many other fields, such as Theoretical Physics, NonlinearDynamics, Mathematical and Theoretical Biology, Neuroscience, the Theory of Cognition, NetworkAnalysis, Economic and Social Systems, History of Science and Philosophy, and a general theoryof Complex Systems from an interdisciplinary perspective. in 2010, he obtained an AdvancedGrant of the European Research Council, the most prestigious research grant in Europe.