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The International Congress of Chinese Mathematicians (ICCM) is an important event among the large international community of mathematicians of Chinese descent. The sixth Congress was held at Taipei, Taiwan in July 2013.Proceedings of the Sixth International Congress of Chinese Mathematicians presents the plenary talks and more than 60 invited talks from the Congress, reflecting the latest developments in mathematics. It is an important reference for researchers in all fields of mathematics, and makes a valuable addition to the collection of a university library.

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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 collection presents the major mathematical works of Isadore Singer, selected by Singer himself, and organized thematically into three volumes: 1. Functional analysis, differential geometry and eigenvalues 2. Index theory 3. Gauge theory and physics Each volume begins with a commentary (and in the first volume, a short biography of Singer), and then presents the works on its theme in roughly chronological order.

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This is the fifteenth issue (Vol. 8, No. 1, July 2020) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization.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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Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2017 at Harvard University.

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One of the most eminent of contemporary mathematicians, Shing-Tung Yau has received numerous honors, including the 1982 Fields Medal, considered the highest honor in mathematics, for his work in differential geometry. He is known also for his work in algebraic and Kähler geometry, general relativity, and string theory. His influence in the development and establishment of these areas of research has been great.These five volumes reproduce a comprehensive selection of his published mathematical papers of the years 1971 to 1991—a period of groundbreaking accomplishments in numerous disciplines including geometric analysis, Kähler geometry, and general relativity.The editors have organized the contents of this collection by subject area—metric geometry and minimal submanifolds; metric geometry and harmonic functions; eigenvalues and general relativity; and Kähler geometry.Also presented are expert commentaries on the subject matter, and personal reminiscences that shed light on the development of the ideas which appear in these papers.

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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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This is the fourteenth issue (Vol. 7, No. 2, December 2019) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization.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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This work presents lectures from the important String Theory International Conference held in 2002 in Hangzhou, China. These include talks given by several mathematicians of particular prominence in the field, among them Stephen Hawking and Edward Witten. Interest in string theory is driven largely by the hope that it will evolve to be the ultimate 'Theory of Everything'. Work on string theory has led to advances in many branches of mathematics. This rapidly developing subject is one of the mainstream topics of mathematics in the 21st century. The current volume presents lectures from the important String Theory International Conference held in 2002 in Hangzhou, China. These include talks given by several mathematicians of particular prominence in the field, among them Stephen Hawking and Edward Witten.

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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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