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John Coleman Moore
John Coleman Moore (May 27, 1923 – January 1, 2016) was an American mathematician. The Borel−Moore homology and Eilenberg–Moore spectral sequence are named after him. Early life and education Moore was born in 1923 in Staten Island, New York. He received his B.A. in 1948 from the Massachusetts Institute of Technology and his Ph.D. in 1952 from Brown University under the supervision of George W. Whitehead. Career Moore began his career at Princeton University as an instructor, and was eventually promoted to full professor in 1961. He retired from Princeton in 1989, after which he took a half-time position at the University of Rochester. His most-cited paper is on Hopf algebras, co-authored with John Milnor. As a faculty member at Princeton University, he advised 24 students and is the academic ancestor of over 1000 mathematicians. He was an Invited Speaker at the International Congress of Mathematicians in 1958 in Edinburgh and in 1970 in Nice. In 1983, a conference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Staten Island
Staten Island ( ) is a borough of New York City, coextensive with Richmond County, in the U.S. state of New York. Located in the city's southwest portion, the borough is separated from New Jersey by the Arthur Kill and the Kill Van Kull and from the rest of New York by New York Bay. With a population of 495,747 in the 2020 Census, Staten Island is the least populated borough but the third largest in land area at . A home to the Lenape indigenous people, the island was settled by Dutch colonists in the 17th century. It was one of the 12 original counties of New York state. Staten Island was consolidated with New York City in 1898. It was formally known as the Borough of Richmond until 1975, when its name was changed to Borough of Staten Island. Staten Island has sometimes been called "the forgotten borough" by inhabitants who feel neglected by the city government. The North Shore—especially the neighborhoods of St. George, Tompkinsville, Clifton, and Stapleton—i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Wayne Thomason
Robert Wayne Thomason (5 November 1952 Tulsa, Oklahoma, U.S. – 5 November 1995, Paris, France) was an American mathematician who worked on algebraic K-theory. His results include a proof that all infinite loop space machines are in some sense equivalent, and progress on the Quillen–Lichtenbaum conjecture. Thomason did his undergraduate studies at Michigan State University, graduating with a B.S. in mathematics in 1973. He completed his Ph.D. at Princeton University in 1977, under the supervision of John Moore. From 1977 to 1979 he was a C. L. E. Moore instructor at the Massachusetts Institute of Technology, and from 1979 to 1982 he was a Dickson Assistant Professor at the University of Chicago. After spending a year at the Institute for Advanced Study, he was appointed as faculty at Johns Hopkins University in 1983. Thomason suffered from diabetes Diabetes, also known as diabetes mellitus, is a group of metabolic disorders characterized by a high blood sugar level ( hype ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nice
Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly 1 millionDemographia: World Urban Areas , Demographia.com, April 2016 on an area of . Located on the , the southeastern coast of France on the , at the foot of the |
Edinburgh
Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian on the southern shore of the Firth of Forth. Edinburgh is Scotland's List of towns and cities in Scotland by population, second-most populous city, after Glasgow, and the List of cities in the United Kingdom, seventh-most populous city in the United Kingdom. Recognised as the capital of Scotland since at least the 15th century, Edinburgh is the seat of the Scottish Government, the Scottish Parliament and the Courts of Scotland, highest courts in Scotland. The city's Holyrood Palace, Palace of Holyroodhouse is the official residence of the Monarchy of the United Kingdom, British monarchy in Scotland. The city has long been a centre of education, particularly in the fields of medicine, Scots law, Scottish law, literature, philosophy, the sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Genealogy
An academic, or scientific genealogy organizes a family tree of scientists and scholars according to mentoring relationships, often in the form of dissertation supervision relationships, and not according to genetic relationships as in conventional genealogy. Since the term ''academic genealogy'' has now developed this specific meaning, its additional use to describe a more academic approach to conventional genealogy would be ambiguous, so the description scholarly genealogy is now generally used in the latter context. Overview The academic lineage or academic ancestry of someone is a chain of professors who have served as academic mentors or thesis advisors of each other, ending with the person in question. Many genealogical terms are often recast in terms of academic lineages, so one may speak of academic descendants, children, siblings, etc. One method of developing an academic genealogy is to organize individuals by prioritizing their degree of relationship to a mentor/ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook University and one of the five mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize (the others being Serre, Thompson, Deligne, and Margulis.) Early life and career Milnor was born on February 20, 1931, in Orange, New Jersey. His father was J. Willard Milnor and his mother was Emily Cox Milnor. As an undergraduate at Princeton University he was named a Putnam Fellow in 1949 and 1950 and also proved the Fáry–Milnor theorem when he was only 19 years old. Milnor graduated with an A.B. in mathematics in 1951 after completing a senior thesis, titled "Link groups", under the supervision of Robert H. Fox. He remained at Princeton to pursue graduate studies and received his Ph.D. in mathematics in 1954 after completi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hopf Algebra
Hopf is a German surname. Notable people with the surname include: *Eberhard Hopf (1902–1983), Austrian mathematician *Hans Hopf (1916–1993), German tenor *Heinz Hopf (1894–1971), German mathematician *Heinz Hopf (actor) (1934–2001), Swedish actor *Ludwig Hopf (1884–1939), German physicist *Maria Hopf Maria Hopf (13 September 1913 – 24 August 2008) was a pioneering archaeobotanist, based at the RGZM, Mainz. Career Hopf studied botany from 1941–44, receiving her doctorate in 1947 on the subject of soil microbes. She then worked in phyto ... (1914-2008), German botanist and archaeologist {{surname, Hopf German-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milnor–Moore Theorem
In algebra, the Milnor–Moore theorem, introduced by classifies an important class of Hopf algebras, of the sort that often show up as cohomology rings in algebraic topology. The theorem states: given a connected, graded, cocommutative Hopf algebra ''A'' over a field of characteristic zero with \dim A_n . In algebraic topology, the term usually refers to the corollary of the aforementioned result, that for a pointed, simply connected space ''X'', the following isomorphism holds: :U(\pi_(\Omega X) \otimes \Q) \cong H_(\Omega X;\Q), where \Omega X denotes the loop space In topology, a branch of mathematics, the loop space Ω''X'' of a pointed topological space ''X'' is the space of (based) loops in ''X'', i.e. continuous pointed maps from the pointed circle ''S''1 to ''X'', equipped with the compact-open topolo ... of ''X'', compare with Theorem 21.5 from . This work may also be compared with that of . References * * * * * * External links * Theorems abou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eilenberg–Moore Spectral Sequence
In mathematics, in the field of algebraic topology, the Eilenberg–Moore spectral sequence addresses the calculation of the homology groups of a pullback over a fibration. The spectral sequence formulates the calculation from knowledge of the homology of the remaining spaces. Samuel Eilenberg and John C. Moore's original paper addresses this for singular homology. Motivation Let k be a field and let H_\ast(-)=H_\ast(-,k) and H^\ast(-)=H^\ast(-,k) denote singular homology and singular cohomology with coefficients in ''k'', respectively. Consider the following pullback E_f of a continuous map ''p'': : \begin E_f &\rightarrow & E \\ \downarrow & & \downarrow\\ X &\rightarrow_ &B\\ \end A frequent question is how the homology of the fiber product, E_f, relates to the homology of ''B'', ''X'' and ''E''. For example, if ''B'' is a point, then the pullback is just the usual product E \times X. In this case the Künneth formula says :H^*(E_f) = H^*(X \times E) \cong H^*(X) \otime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
