Search results for ""Author Lizhen Ji""

The uniformization theorem of Riemann surfaces is one of the most beautiful and important theorems in mathematics. Besides giving a clean classification of Riemann surfaces, its proof has motivated many new methods, such as the Riemann–Hilbert correspondence, Picard–Fuchs equations, and higher-dimensional generalizations of the uniformization theorem, which include Calabi–Yau manifolds.This volume consists of expository papers on the four topics in its title, written by experts from around the world, and is the first to put forth a comprehensive discussion of these topics, and of the relations between them. As such, it is valuable as an introduction for beginners, and as a reference for mathematicians in general.

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This is the thirteenth issue (Vol. 7, No. 1, July 2019) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization.This special issue honors Shing-Tung Yau on the occasion of his 70th birthday.Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education.Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

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In algebraic geometry and theoretical physics, mirror symmetry refers to the relationship between two Calabi–Yau manifolds which appear very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.Mathematicians became interested in mirror symmetry around 1990, when it was shown that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a long-standing problem.Today, mirror symmetry is a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of quantum field theory, the formalism that physicists use to describe elementary particles. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow.This handbook surveys recent developments in mirror symmetry. It presents papers based on selected lectures given at a 2014 Taipei conference on “Calabi–Yau Geometry and Mirror Symmetry,” along with other contributions from invited authors.

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