|
Ralph Louis 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, 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 a ... [...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] |
