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Ralph Cohen
Ralph Louis Cohen (born 1952) is an American mathematician, specializing in algebraic topology and differential topology. Career Cohen received his bachelor's degree from the University of Michigan in 1973 and his Ph.D. in 1978 from Brandeis University where he worked under the supervision of Edgar H. Brown, Jr. His thesis was titled ''On Odd Primary Stable Homotopy Theory''. He did his postdoctoral training as an L.E. Dickson Instructor at the University Chicago, and then became an Assistant Professor of Mathematics at Stanford University in 1980. In 1983, he became an Associate Professor and was promoted to Full Professor in 1987. Cohen is now the Barbara Kimball Browning Professor of Mathematics at Stanford. He was Chair of the Mathematics Department from 1992 to 1995, from 1999 to 2009 he was the Director of the Mathematics Research Center at Stanford, and from 2010 to 2016 was the Senior Associate Dean for the Natural Sciences in the School of Humanities and Sciences. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up to homeomorphism, though usually most classify up to Homotopy#Homotopy equivalence and null-homotopy, homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Main branches of algebraic topology Below are some of the main areas studied in algebraic topology: Homotopy groups In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Whitney Immersion Theorem
In differential topology, the Whitney immersion theorem (named after Hassler Whitney) states that for m>1, any smooth m-dimensional manifold (required also to be Hausdorff and second-countable) has a one-to-one immersion in Euclidean 2m-space, and a (not necessarily one-to-one) immersion in (2m-1)-space. Similarly, every smooth m-dimensional manifold can be immersed in the 2m-1-dimensional sphere (this removes the m>1 constraint). The weak version, for 2m+1, is due to transversality (general position, dimension counting): two ''m''-dimensional manifolds in \mathbf^ intersect generically in a 0-dimensional space. Further results William S. Massey went on to prove that every ''n''-dimensional manifold is cobordant to a manifold that immerses in S^ where a(n) is the number of 1's that appear in the binary expansion of n. In the same paper, Massey proved that for every ''n'' there is manifold (which happens to be a product of real projective spaces) that does not immerse in S^. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kathryn Hess
Kathryn Pamela Hess (born 1967) is an American mathematician who has served as professor of mathematics at École Polytechnique Fédérale de Lausanne (EPFL) since 1999. She is known for her work on homotopy theory, category theory, and algebraic topology, both pure and applied. In particular, she applies the methods of algebraic topology to the study of neurology, cancer biology, and materials science. She is a fellow of the American Mathematical Society. Life Kathryn Hess was born 21 September 1967 in Bryn Mawr, Pennsylvania. She began to accelerate in mathematics in 1979, thanks to the Mathematical Talent Development Project (MTDP) set up in Eau Claire, Wisconsin, by her parents, through the Association for High Potential Children, which they also founded. Both programs are currently defunct. Hess earned a BSc with honors in mathematics from the University of Wisconsin–Madison in 1985. She received her doctorate in mathematics from the Massachusetts Institute of Technology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Annalen
''Mathematische Annalen'' (abbreviated as ''Math. Ann.'' or, formerly, ''Math. Annal.'') is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann. Subsequent managing editors were Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück, and Nigel Hitchin. Currently, the managing editor of Mathematische Annalen is Thomas Schick. Volumes 1–80 (1869–1919) were published by Teubner. Since 1920 (vol. 81), the journal has been published by Springer. In the late 1920s, under the editorship of Hilbert, the journal became embroiled in controversy over the participation of L. E. J. Brouwer on its editorial board, a spillover from the foundational Brouwer–Hilbert controversy. Between 1945 and 1947 the journal briefly ceased publication. References External links''Mathematische Annalen''homepage at Springer''Mathematische Annalen''archive (1869†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Mathematica
''Acta Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research journals".. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 4.273, ranking it 5th out of 330 journals in the category "Mathematics". Publication history The journal was established by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences. The journal was printed and distributed by Springer from 2006 to 2016. Since 2017, Acta Mathematica has been published electronically and in print by International Press. Its electronic version is open access without publishing fees. Poincaré episode The journal's "most famous episode" (according to Villani) concerns Henri Poincaré, who won a prize offered ... [...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] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warsaw
Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officially estimated at 1.86 million residents within a greater metropolitan area of 3.1 million residents, which makes Warsaw the 7th most-populous city in the European Union. The city area measures and comprises 18 districts, while the metropolitan area covers . Warsaw is an Alpha global city, a major cultural, political and economic hub, and the country's seat of government. Warsaw traces its origins to a small fishing town in Masovia. The city rose to prominence in the late 16th century, when Sigismund III decided to move the Polish capital and his royal court from Kraków. Warsaw served as the de facto capital of the Polish–Lithuanian Commonwealth until 1795, and subsequently as the seat of Napoleon's Duchy of Warsaw. Th ... [...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] |
Sloan Research 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 Stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dennis Sullivan
Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center and is a distinguished professor at Stony Brook University. Sullivan was awarded the Wolf Prize in Mathematics in 2010 and the Abel Prize in 2022. Early life and education Sullivan was born in Port Huron, Michigan, on February 12, 1941.. His family moved to Houston soon afterwards. He entered Rice University to study chemical engineering but switched his major to mathematics in his second year after encountering a particularly motivating mathematical theorem. The change was prompted by a special case of the uniformization theorem, according to which, in his own words: He received his Bachelor of Arts degree from Rice in 1963. He obtained his Doctor of Philosophy from Princeton University in 1966 with his thesis, ''Triangulating h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Topology
String topology, a branch of mathematics, is the study of algebraic structures on the homology of free loop spaces. The field was started by . Motivation While the singular cohomology of a space has always a product structure, this is not true for the singular homology of a space. Nevertheless, it is possible to construct such a structure for an oriented manifold M of dimension d. This is the so-called intersection product. Intuitively, one can describe it as follows: given classes x\in H_p(M) and y\in H_q(M), take their product x\times y \in H_(M\times M) and make it transversal to the diagonal M\hookrightarrow M\times M. The intersection is then a class in H_(M), the intersection product of x and y. One way to make this construction rigorous is to use stratifolds. Another case, where the homology of a space has a product, is the (based) loop space \Omega X of a space X. Here the space itself has a product :m\colon \Omega X\times \Omega X \to \Omega X by going first through the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
