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Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to ...
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol . Given two linearly independent vectors a and b, the cross product, a × b ...
Doctoral advisor. Hung-Hsi Wu. Paul C. Yang ( Chinese: 杨建平; pinyin: Yáng Jiàn Píng; Wade–Giles: Chien-Ping Yang ,1947 in Changhua, Taiwan) is a Taiwanese-American mathematician specializing in differential geometry, partial differential equations and CR manifolds. He is best known for his work in Conformal geometry for his study of ...
In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series. is geometric, because each successive term can be obtained by multiplying the previous term by .
Xiuxiong Chen ( Chinese: 陈秀雄; pinyin: Chén Xiùxióng) is a Chinese-American [citation needed] mathematician whose research concerns differential geometry and differential equations. [1] A professor at Stony Brook University since 2010, he was elected a Fellow of the American Mathematical Society in 2015 and awarded the Oswald Veblen ...
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic ...
Website. www .ams .org /prizes /veblen-prize .html. The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was funded in 1961 in memory of Oswald Veblen and first issued in 1964. The Veblen Prize is now worth US$5000, and is awarded every three years.
Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms. The term "synthetic geometry" was coined only after the 17th century ...