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From Riemann and Kodaira to Modern Developments on Complex Manifolds

  • Takagi Lectures
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Japanese Journal of Mathematics Aims and scope

Abstract

We survey the theory of complex manifolds that are related to Riemann surface, Hodge theory, Chern class, Kodaira embedding and Hirzebruch–Riemann–Roch, and some modern development of uniformization theorems, Kähler–Einstein metric and the theory of Donaldson–Uhlenbeck–Yau on Hermitian Yang–Mills connections. We emphasize mathematical ideas related to physics. At the end, we identify possible future research directions and raise some important open questions.

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  1. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA, 02138, USA

    Shing-Tung Yau

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Communicated by: Hiraku Nakajima

This article is based on the 16th Takagi Lectures that the author delivered at the University of Tokyo on November 28 and 29, 2015.

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Yau, ST. From Riemann and Kodaira to Modern Developments on Complex Manifolds. Jpn. J. Math. 11, 265–303 (2016). https://doi.org/10.1007/s11537-016-1565-6

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