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Lefschetz Motive
Solomon Lefschetz (russian: Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations. Life He was born in Moscow, the son of Alexander Lefschetz and his wife Sarah or Vera Lifschitz, Jewish traders who used to travel around Europe and the Middle East (they held Ottoman Empire, Ottoman passports). Shortly thereafter, the family moved to Paris. He was educated there in engineering at the École Centrale Paris, but emigrated to the US in 1905. He was badly injured in an industrial accident in 1907, losing both hands. He moved towards mathematics, receiving a Doctor of Philosophy, Ph.D. in algebraic geometry from Clark University in Worcester, Massachusetts in 1911. He then took positions in University of Nebraska and University of Kansas, moving to Princeton University in 1924, where he was soo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ralph Fox
Ralph Hartzler Fox (March 24, 1913 – December 23, 1973) was an American mathematician. As a professor at Princeton University, he taught and advised many of the contributors to the ''Golden Age of differential topology'', and he played an important role in the modernization and main-streaming of knot theory. Biography Ralph Fox attended Swarthmore College for two years, while studying piano at the Leefson Conservatory of Music in Philadelphia. He earned a master's degree from Johns Hopkins University, and a PhD degree from Princeton University in 1939. His doctoral dissertation, ''On the Lusternick-Schnirelmann Category'', was directed by Solomon Lefschetz. (In later years he disclaimed all knowledge of the Lusternik–Schnirelmann category, and certainly never published on the subject again.) He directed 21 doctoral dissertations, including those of John Milnor, John Stallings, Francisco González-Acuña, Guillermo Torres-Diaz and Barry Mazur, and supervised Ken ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lefschetz Fixed-point Theorem
In mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X. It is named after Solomon Lefschetz, who first stated it in 1926. The counting is subject to an imputed multiplicity at a fixed point called the fixed-point index. A weak version of the theorem is enough to show that a mapping without ''any'' fixed point must have rather special topological properties (like a rotation of a circle). Formal statement For a formal statement of the theorem, let :f\colon X \rightarrow X\, be a continuous map from a compact triangulable space X to itself. Define the Lefschetz number \Lambda_f of f by :\Lambda_f:=\sum_(-1)^k\mathrm(f_*, H_k(X,\Q)), the alternating (finite) sum of the matrix traces of the linear maps induced by f on H_k(X,\Q), the singular homology groups of X with rational coefficients. A simple vers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvia De Neymet
Sylvia de Neymet Urbina (aka Silvia de Neymet de Christ, 1939 – 13 January 2003) was a Mexican mathematician, the first woman to earn a doctorate in mathematics in Mexico, and the first female professor in the faculty of sciences of the National Autonomous University of Mexico (UNAM). Early life and education De Neymet was born in Mexico City in 1939. Her mother had been orphaned in the Mexican Revolution of 1910, studied art at La Esmeralda, and became a teacher; she encouraged De Neymet in her studies. Her father's mother was also a teacher, and her father was a civil engineer. In 1955 she began studying at the Universidad Femenina de México, a women's school founded by , and in her fourth year there she was hired as a mathematics teacher herself, despite the fact that many of her students would be older than her. After two years of mathematical study in Paris, at the Institut Henri Poincaré, from 1959 to 1961, de Neymet returned to Mexico and was given a degree in mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Wallman
Henry "Hank" Wallman (1915Biography of Wallman at the (in Swedish).–1992) was an American mathematician, known for his work in , , , and |
John Tukey
John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term 'bit' and the first published use of the word 'software'. Biography Tukey was born in New Bedford, Massachusetts in 1915, to a Latin teacher father and a private tutor. He was mainly taught by his mother and attended regular classes only for certain subjects like French. Tukey obtained a BA in 1936 and MSc in 1937 in chemistry, from Brown University, before moving to Princeton University, where in 1939 he received a PhD in mathematics after completing a doctoral dissertation titled "On denumerability in topology". During World War II, Tukey worked at the Fire Control Research Office and collaborated wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert W
Albert may refer to: Companies * Albert (supermarket), a supermarket chain in the Czech Republic * Albert Heijn, a supermarket chain in the Netherlands * Albert Market, a street market in The Gambia * Albert Productions, a record label * Albert Computers, Inc., a computer manufacturer in the 1980s Entertainment * ''Albert'' (1985 film), a Czechoslovak film directed by František Vláčil * ''Albert'' (2015 film), a film by Karsten Kiilerich * ''Albert'' (2016 film), an American TV movie * ''Albert'' (Ed Hall album), 1988 * "Albert" (short story), by Leo Tolstoy * Albert (comics), a character in Marvel Comics * Albert (''Discworld''), a character in Terry Pratchett's ''Discworld'' series * Albert, a character in Dario Argento's 1977 film ''Suspiria'' Military * Battle of Albert (1914), a WWI battle at Albert, Somme, France * Battle of Albert (1916), a WWI battle at Albert, Somme, France * Battle of Albert (1918), a WWI battle at Albert, Somme, France People * Albert (given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Truesdell
Clifford Ambrose Truesdell III (February 18, 1919 – January 14, 2000) was an American mathematician, natural philosopher, and historian of science. Life Truesdell was born in Los Angeles, California. After high school, he spent two years in Europe learning French, German, and Italian, and improving his Latin and Greek. His linguistic skills stood him in good stead in his later historical investigations. At Caltech he was deeply influenced by the teaching of Harry Bateman. In particular, a course in partial differential equations "taught me the difference between an ordinary good teacher and a great mathematician, and after that I never cared what grade I got in anything." He obtained a B.Sc. in mathematics and physics in 1941, and an MSc. in mathematics in 1942. In 1943, he completed a Ph.D. in mathematics at Princeton University. For the rest of the decade, the U.S. Navy employed him to do mechanics research. Truesdell taught at Indiana University 1950–61, where his students ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Harold Stone
Arthur Harold Stone (30 September 1916 – 6 August 2000) was a British mathematician born in London, who worked at the universities of Manchester and Rochester, mostly in topology. His wife was American mathematician Dorothy Maharam. Stone studied at Trinity College, Cambridge. His first paper dealt with squaring the square, he proved the Erdős–Stone theorem with Paul Erdős and is credited with the discovery of the first two flexagons, a trihexaflexagon and a hexahexaflexagon while he was a student at Princeton University in 1939. His Ph.D. thesis, ''Connectedness and Coherence'', was written in 1941 under the direction of Solomon Lefschetz. He served as a referee for ''The American Mathematical Monthly'' journal in the 1980s. The Stone metrization theorem has been named after him, and he was a member of a group of mathematicians who published pseudonymously as Blanche Descartes. He is not to be confused with American mathematician Marshall Harvey Stone. See also *Ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norman Steenrod
Norman Earl Steenrod (April 22, 1910October 14, 1971) was an American mathematician most widely known for his contributions to the field of algebraic topology. Life He was born in Dayton, Ohio, and educated at Miami University and University of Michigan (A.B. 1932). After receiving a master's degree from Harvard University in 1934, he enrolled at Princeton University. He completed his Ph.D. under the direction of Solomon Lefschetz, with a thesis titled ''Universal homology groups''. Steenrod held positions at the University of Chicago from 1939 to 1942, and the University of Michigan from 1942 to 1947. He moved to Princeton University in 1947, and remained on the Faculty there for the rest of his career. He was editor of the Annals of Mathematics and a member of the National Academy of Sciences. He died in Princeton, survived by his wife, the former Carolyn Witter, and two children. Work Thanks to Lefschetz and others, the cup product structure of cohomology was understood by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul A
Paul may refer to: *Paul (given name), a given name (includes a list of people with that name) *Paul (surname), a list of people People Christianity *Paul the Apostle (AD c.5–c.64/65), also known as Saul of Tarsus or Saint Paul, early Christian missionary and writer *Pope Paul (other), multiple Popes of the Roman Catholic Church *Saint Paul (other), multiple other people and locations named "Saint Paul" Roman and Byzantine empire *Lucius Aemilius Paullus Macedonicus (c. 229 BC – 160 BC), Roman general *Julius Paulus Prudentissimus (), Roman jurist *Paulus Catena (died 362), Roman notary *Paulus Alexandrinus (4th century), Hellenistic astrologer *Paul of Aegina or Paulus Aegineta (625–690), Greek surgeon Royals *Paul I of Russia (1754–1801), Tsar of Russia *Paul of Greece (1901–1964), King of Greece Other people *Paul the Deacon or Paulus Diaconus (c. 720 – c. 799), Italian Benedictine monk *Paul (father of Maurice), the father of Maurice, Byzan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
