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Kefeng Liu
Kefeng Liu (Chinese: 刘克峰; born 12 December 1965), is a Chinese-American mathematician who is known for his contributions to geometric analysis, particularly the geometry, topology and analysis of moduli spaces of Riemann surfaces and Calabi–Yau manifolds. He is a professor of mathematics at University of California, Los Angeles, as well as the executive director of the Center of Mathematical Sciences at Zhejiang University. He is best known for his collaboration with Bong Lian and Shing-Tung Yau in which they establish some enumerative geometry conjectures motivated by mirror symmetry. Biography Liu was born in Kaifeng, Henan province, China. In 1985, Liu received his B.A. in mathematics from the Department of Mathematics of Peking University in Beijing. In 1988, Liu obtained his M.A. from the Institute of Mathematics of the Chinese Academy of Sciences (CAS) in Beijing. Liu then went to study in the United States, obtaining a Ph.D. from Harvard University in 1993 under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaifeng
Kaifeng () is a prefecture-level city in east-central Henan province, China. It is one of the Eight Ancient Capitals of China, having been the capital eight times in history, and is best known for having been the Chinese capital during the Northern Song dynasty. As of 31 December 2018, around 4,465,000 people lived in Kaifeng's Prefecture, of whom 1,652,000 lived in the built-up (or metro) area made of Xiangfu, Longting, Shunhe Hui, Gulou and Yuwantai Districts. Located along the Yellow River's southern bank, it borders the provincial capital of Zhengzhou to the west, Xinxiang to the northwest, Shangqiu to the east, Zhoukou to the southeast, Xuchang to the southwest, and Heze of Shandong to the northeast. Kaifeng is also a major city in the world by scientific research outputs as tracked by the Nature Index. The city is home to a campus of Henan University, one of the national key universities in the Double First Class University Plan. Names The postal romanization for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Surfaces
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. The main interest in Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm. Every Riemann surface is a two-dimensional real analytic manifold (i.e., a surface), but it contains more structure (specifically a complex structure) which is needed for the unambiguous definition of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guggenheim Fellowship
Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation issues awards in each of two separate competitions: * One open to citizens and permanent residents of the United States and Canada. * The other to citizens and permanent residents of Latin America and the Caribbean. The Latin America and Caribbean competition is currently suspended "while we examine the workings and efficacy of the program. The U.S. and Canadian competition is unaffected by this suspension." The performing arts are excluded, although composers, film directors, and choreographers are eligible. The fellowships are not open to students, only to "advanced professionals in mid-career" such as published authors. The fellows may spend the money as they see fit, as the purpose is to give fellows "b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sloan Fellowship
The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. Fellowships were initially awarded in physics, chemistry, and mathematics. Awards were later added in neuroscience (1972), economics (1980), computer science (1993), computational and evolutionary molecular biology (2002), and ocean sciences or earth systems sciences (2012). Winners of these two-year fellowships are awarded $75,000, which may be spent on any expense supporting their research. From 2012 through 2020, the foundation awarded 126 research fellowship each year; in 2021, 128 were awarded, and 118 were awarded in 2022. Eligibility and selection To be eligible, a candidate must hold a Ph.D. or equivalent degree and must be a member of the faculty of a college, university, or other degree-granting institution in the United Sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considered among the most prestigious universities in the world. Stanford was founded in 1885 by Leland and Jane Stanford in memory of their only child, Leland Stanford Jr., who had died of typhoid fever at age 15 the previous year. Leland Stanford was a U.S. senator and former governor of California who made his fortune as a railroad tycoon. The school admitted its first students on October 1, 1891, as a coeducational and non-denominational institution. Stanford University struggled financially after the death of Leland Stanford in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, provost of Stanford Frederick Terman inspired and supported faculty and graduates' entrepreneu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assistant Professor
Assistant Professor is an academic rank just below the rank of an associate professor used in universities or colleges, mainly in the United States and Canada. Overview This position is generally taken after earning a doctoral degree and generally after several years of holding one or more Postdoctoral Researcher positions. It is below the position of Associate Professor at most universities and is equivalent to the rank of Lecturer at most Commonwealth universities. In the United States, Assistant Professor is often the first position held in a tenure track, although it can also be a non-tenure track position. A typical professorship sequence is Assistant Professor, Associate Professor, and Full Professor in order. After 7 years, if successful, Assistant Professors can get tenure and also get promotion to Associate Professor. There is high demand for vacant tenure-track Assistant Professor positions, often with hundreds of applicants. Less than 20% of doctoral graduates move ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beijing
} Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 million residents. It has an administrative area of , the third in the country after Guangzhou and Shanghai. It is located in Northern China, and is governed as a municipality under the direct administration of the State Council with 16 urban, suburban, and rural districts.Figures based on 2006 statistics published in 2007 National Statistical Yearbook of China and available online at archive. Retrieved 21 April 2009. Beijing is mostly surrounded by Hebei Province with the exception of neighboring Tianjin to the southeast; together, the three divisions form the Jingjinji megalopolis and the national capital region of China. Beijing is a global city and one of the world's leading centres for culture, diplomacy, politics, finance, busi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People's Republic Of China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and borders fourteen countries by land, the most of any country in the world, tied with Russia. Covering an area of approximately , it is the world's third largest country by total land area. The country consists of 22 provinces, five autonomous regions, four municipalities, and two Special Administrative Regions (Hong Kong and Macau). The national capital is Beijing, and the most populous city and financial center is Shanghai. Modern Chinese trace their origins to a cradle of civilization in the fertile basin of the Yellow River in the North China Plain. The semi-legendary Xia dynasty in the 21st century BCE and the well-attested Shang and Zhou dynasties developed a bureaucratic political system to serve hereditary monarchies, or dyna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henan Province
Henan (; or ; ; alternatively Honan) is a landlocked province of China, in the central part of the country. Henan is often referred to as Zhongyuan or Zhongzhou (), which literally means "central plain" or "midland", although the name is also applied to the entirety of China proper. Henan is a birthplace of Han Chinese civilization, with over 3,200 years of recorded history and remained China's cultural, economic and political center until approximately 1,000 years ago. Henan Province is home to many heritage sites, including the ruins of Shang dynasty capital city Yin and the Shaolin Temple. Four of the Eight Great Ancient Capitals of China, Luoyang, Anyang, Kaifeng and Zhengzhou, are in Henan. The practice of tai chi also began here in Chen Jia Gou Village (Chen style), as did the later Yang and Wu styles. Although the name of the province () means "south of the ellowriver.", approximately a quarter of the province lies north of the Yellow River, also known as the H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mirror Symmetry
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric. In conclusion, a line of symmetry splits the shape in half and those halves should be identical. Symmetric function In formal terms, a mathematical object is symmetric with respect to a given operation such as reflection, rotation or translation, if, when applied to the object, this operation preserves some property of the object. The set of operations that preserve a given property of the object form a group. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by some of the operations (and vice versa). The symm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enumerative Geometry
In mathematics, enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions, mainly by means of intersection theory. History The problem of Apollonius is one of the earliest examples of enumerative geometry. This problem asks for the number and construction of circles that are tangent to three given circles, points or lines. In general, the problem for three given circles has eight solutions, which can be seen as 23, each tangency condition imposing a quadratic condition on the space of circles. However, for special arrangements of the given circles, the number of solutions may also be any integer from 0 (no solutions) to six; there is no arrangement for which there are seven solutions to Apollonius' problem. Key tools A number of tools, ranging from the elementary to the more advanced, include: * Dimension counting * Bézout's theorem * Schubert calculus, and more generally characteristic classes in cohomology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
