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Calabi
Eugenio Calabi (May 11, 1923 – September 25, 2023) was an Italian-born American mathematician and the Thomas A. Scott Professorship of Mathematics, Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications. Early life and education Calabi was born in Milan, Milan, Italy on May 11, 1923, into a Italian Jews, Jewish family. His sister was the journalist Tullia Zevi, Tullia Zevi Calabi. In 1938, the family left Italy because of the Italian racial laws, racial laws, and in 1939 arrived in the United States. In the fall of 1939, aged only 16, Calabi enrolled at the Massachusetts Institute of Technology, studying chemical engineering. His studies were interrupted when he was Conscription in the United States, drafted in the US military in 1943 and served during World War II. Upon his discharge in 1946, Calabi was able to finish his bachelor's degree under the G.I. Bill, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calabi–Yau Manifold
In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has certain properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry. Their name was coined by , after , who first conjectured that compact complex manifolds of Kähler type with vanishing first Chern class always admit Ricci-flat Kähler metrics, and , who proved the Calabi conjecture. Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex dimensions (i.e. any even number of real dimensions). They were originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calabi Conjecture
In the mathematical field of differential geometry, the Calabi conjecture was a conjecture about the existence of certain kinds of Riemannian metrics on certain complex manifolds, made by . It was proved by , who received the Fields Medal and Oswald Veblen Prize in part for his proof. His work, principally an analysis of an elliptic partial differential equation known as the complex Monge–Ampère equation, was an influential early result in the field of geometric analysis. More precisely, Calabi's conjecture asserts the resolution of the prescribed Ricci curvature problem within the setting of Kähler metrics on closed complex manifolds. According to Chern–Weil theory, the Ricci form of any such metric is a closed differential 2-form which represents the first Chern class. Calabi conjectured that for any such differential form , there is exactly one Kähler metric in each Kähler class whose Ricci form is . (Some compact complex manifolds admit no Kähler classes, in w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calabi Triangle
The Calabi triangle is a special triangle found by Eugenio Calabi and defined by its property of having three different placements for the largest square that it contains. It is an isosceles triangle which is obtuse triangle, obtuse with an irrational number, irrational but algebraic number, algebraic ratio between the lengths of its sides and its base. Definition Consider the largest square that can be placed in an arbitrary triangle. It may be that such a square could be positioned in the triangle in more than one way. If the largest such square can be positioned in three different ways, then the triangle is either an equilateral triangle or the Calabi triangle. Thus, the Calabi triangle may be defined as a triangle that is not equilateral and has three placements for its largest square. Shape The triangle is isosceles which has the same length of sides as . If the ratio of the base to either leg is , we can set that . Then we can consider the following three cases: ;case 1) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calabi Flow
In the mathematical fields of differential geometry and geometric analysis, the Calabi flow is a geometric flow which deforms a Kähler metric on a complex manifold. Precisely, given a Kähler manifold , the Calabi flow is given by: :\frac=\frac, where is a mapping from an open interval into the collection of all Kähler metrics on , is the scalar curvature of the individual Kähler metrics, and the indices correspond to arbitrary holomorphic coordinates . This is a fourth-order geometric flow, as the right-hand side of the equation involves fourth derivatives of . The Calabi flow was introduced by Eugenio Calabi in 1982 as a suggestion for the construction of extremal Kähler metrics, which were also introduced in the same paper. It is the gradient flow of the '; extremal Kähler metrics are the critical points of the Calabi functional. A convergence theorem for the Calabi flow was found by Piotr Chruściel in the case that has complex dimension equal to one. Xiuxiong Che ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calabi–Eckmann Manifold
In complex geometry, a part of mathematics, a Calabi–Eckmann manifold (or, often, Calabi–Eckmann space), named after Eugenio Calabi and Beno Eckmann, is a complex, homogeneous, non-Kähler manifold, homeomorphic to a product of two odd-dimensional spheres of dimension ≥ 3. The Calabi–Eckmann manifold is constructed as follows. Consider the space ^n\backslash \ \times ^m\backslash \, where m,n>1, equipped with an action of the group : : t\in , \ (x,y)\in ^n\backslash \ \times ^m\backslash \ \mid t(x,y)= (e^tx, e^y) where \alpha\in \backslash is a fixed complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for .... It is easy to check that this action is free and proper, and the corresponding orbit space ''M'' is homeomorphic to S^\times S^. Since ''M'' is a quot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tullia Zevi
Tullia Zevi (née Calabi; 2 February 1919 – 22 January 2011) was an Italian journalist and writer. Zevi's family fled Italy to France and then to the US after the rise of fascism in the 1930s. While in New York City, she married Bruno Zevi. She returned to Europe in 1946, and was one of the few women journalists to report the Nuremberg Trials. On her return to Italy, she played a major role in Interfaith dialog, and was active in Italian Centre-left politics. Zevi was president of the Union of Italian Jewish Communities from 1983 to 1998. Biography Zevi was born in Milan, one of four children of an upper middle-class Jewish-Italian family. Her father Giuseppe Calabi was a lawyer and prominent anti-fascist. Her brother was the mathematician Eugenio Calabi. Zevi studied philosophy at the University of Milan and studied music at the Milan Conservatory. When the Fascist government of Italy passed anti-Jewish laws, Zevi was on holiday in Switzerland with her family. Later ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Xiu-Xiong Chen
Xiuxiong Chen () is a Chinese-American mathematician whose research concerns differential geometry and differential equations. Professor at Stony Brook University since 2010, he was elected a Fellow of the American Mathematical Society in 2015 and awarded the Oswald Veblen Prize in Geometry in 2019. In 2019, he was awarded the Simons Investigator award. Biography Chen was born in Qingtian County, Zhejiang, China. He entered the Department of Mathematics of the University of Science and Technology of China in 1982, and graduated in 1987. He subsequently studied under Peng Jiagui (彭家贵) at the Graduate School of the Chinese Academy of Sciences, where he earned his master's degree. In 1989, he moved to the United States to study at the University of Pennsylvania. The last doctoral student of Eugenio Calabi, he obtained his Ph.D. in mathematics in 1994, with his dissertation on "Extremal Hermitian Matrices with Curvature Distortion in a Riemann Surface". Chen was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Putnam Fellow
The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regardless of the students' nationalities). It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools, plus one of the top five individual scorers (designated as ''Putnam Fellows'') is awarded a scholarship of up to $12,000 plus tuition at Harvard University (Putnam Fellow Prize Fellowship), the top 100 individual scorers have their names mentioned in the American Mathematical Monthly (alphabetically ordered within rank), and the names and addresses of the top 500 contestants are mailed to all participating institutions. It is widely considered to be the most prestigious university-level mathematics competition in the world, and its difficulty is such that the median score ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salomon Bochner
Salomon Bochner (20 August 1899 – 2 May 1982) was a Galizien-born mathematician, known for work in mathematical analysis, probability theory and differential geometry. Life He was born into a Jewish family in Podgórze (near Kraków), then Austria-Hungary, now Poland. Fearful of a Russian invasion in Galicia at the beginning of World War I in 1914, his family moved to Germany, seeking greater security. Bochner was educated at a Berlin gymnasium (secondary school), and then at the University of Berlin. There, he was a student of Erhard Schmidt, writing a dissertation involving what would later be called the Bergman kernel. Shortly after this, he left the academy to help his family during the escalating inflation. After returning to mathematical research, he lectured at the University of Munich from 1924 to 1933. His academic career in Germany ended after the Nazis came to power in 1933, and he left for a position at Princeton University. He was a visiting scholar at th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Lowell Putnam Mathematical Competition
The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual list of mathematics competitions, mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regardless of the students' nationalities). It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools, plus one of the top five individual scorers (designated as ''#Putnam_Fellows, Putnam Fellows'') is awarded a scholarship of up to $12,000 plus tuition at Harvard University (Putnam Fellow Prize Fellowship), the top 100 individual scorers have their names mentioned in the American Mathematical Monthly (alphabetically ordered within rank), and the names and addresses of the top 500 contestants are mailed to all participating institutions. It is widely considered to be the most prestigious university-level mathematics competition in the world, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italian Jews
Italian Jews (; ) or Roman Jews (; ) can be used in a broad sense to mean all Jews living in or with roots in Italy, or, in a narrower sense, to mean the Italkim, an ancient community living in Italy since the Ancient Roman era, who use the Italian liturgy (or " Italian Rite") as distinct from those Jewish communities in Italy dating from medieval or modern times who use the Sephardic liturgy or the Nusach Ashkenaz. Name Italkim have descent from the Jews who lived in Italy during the Roman period. Their Nusach is distinct from the Sephardic Nusach and the Ashkenazi Nusach, and are sometimes referred to in the scholarly literature as ''Italkim'' (Hebrew for "Italians"; pl. of , Middle Hebrew loanword from the Latin adjective , meaning "Italic", "Latin", "Roman"; is also used in Modern Hebrew as the word for "Italian language" (singular). They have traditionally spoken a variety of Judeo-Italian languages. Divisions Italian Jews historically fall into four categories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Pennsylvania School Of Arts And Sciences
The University of Pennsylvania School of Arts and Sciences (also known as SAS) is the academic institution encompassing the humanities, social sciences, and natural sciences at the University of Pennsylvania. Formerly known as the Faculty of Arts and Sciences, SAS is an umbrella organization that is divided into three main academic components: The College of Arts & Sciences (CAS) is Penn's undergraduate liberal arts school. The Graduate Division offers post-undergraduate M.A., M.S., and Ph.D. programs. The College of Liberal and Professional Studies (LPS), originally called the College of General Studies, is Penn's professional education division catering to working professionals. Professor Steven J. Fluharty has been the school's dean since July 2013. History The 1755 charter of Benjamin Franklin's College of Philadelphia paved the way to form the College of Arts and Sciences, which was originally for men only. In 1933, Penn established the College of Liberal Arts for Women ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
