|
Michel Kervaire
Michel André Kervaire (26 April 1927 – 19 November 2007) was a French mathematician who made significant contributions to topology and algebra. He introduced the Kervaire semi-characteristic. He was the first to show the existence of topological ''n''-manifolds with no differentiable structure (using the Kervaire invariant), and (with John Milnor) computed the number of exotic spheres in dimensions greater than four, known as Kervaire–Milnor groups. He is also well known for fundamental contributions to high-dimensional knot theory. The solution of the Kervaire invariant problem was announced by Michael Hopkins in Edinburgh on 21 April 2009. Education He was the son of André Kervaire (a French industrialist) and Nelly Derancourt. After completing high school in France, Kervaire pursued his studies at ETH Zurich (1947–1952), receiving a Ph.D. in 1955. His thesis, entitled ''Courbure intégrale généralisée et homotopie'', was written under the direction of Heinz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Częstochowa
Częstochowa ( , ) is a city in southern Poland on the Warta with 214,342 inhabitants, making it the thirteenth-largest city in Poland. It is situated in the Silesian Voivodeship. However, Częstochowa is historically part of Lesser Poland, not Silesia, and before the Partitions of Poland, 1795 Partition of Poland, it belonged to the Kraków Voivodeship (14th century – 1795), Kraków Voivodeship. Częstochowa is located in the Kraków-Częstochowa Upland. It is the largest economic, cultural and administrative hub in the northern part of the Silesian Voivodeship. The city is known for the famous Jasna Góra Monastery of the Order of Saint Paul the First Hermit of the Catholic Church, which is the home of the Black Madonna of Częstochowa, a shrines to Mary, mother of Jesus, shrine to Mary, mother of Jesus. Every year, millions of pilgrims from all over the world come to Częstochowa to see it. Częstochowa was also home to Frankism in the late 18th and 19th centuries, an antinom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Torsion (mechanics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a Set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of List of continuity-related mathematical topics, continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and Homotopy, homotopies. A property that is invariant under such deformations is a to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Swiss Mathematical Society
The Swiss Mathematical Society, SMS (, SMG; ), founded in Basel on 4 September 1910, is the national mathematical society of Switzerland. It is a member of the European Mathematical Society. History The SMS was established on 4 September 1910 in Basel as a specialised section of the Swiss Natural Research Society (SNG). Initiated by Rudolf Fueter, Henri Fehr and Marcel Grossmann, a circular signed by nineteen leading mathematicians drew eighty-two founding members, and the constitutive meeting was held that afternoon in the . From its earliest years the SMG organised annual spring and autumn sectional meetings—initially within the SNG framework—at which members presented research and exchange of ideas. Membership fees began at Swiss franc, CHF 2 per annum (later rising in stages and, from 2007, incorporating a reduced student rate) and the Society's governing statutes provided for a rotating presidency via an executive of three elected officers. In 1928 the SMG resolved to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Neuchâtel
The University of Neuchâtel (UniNE) is a French-speaking public research university in Neuchâtel, Switzerland. The university has four faculties (schools) and more than a dozen institutes, including arts and human sciences, natural sciences, law and economics. The Faculty of Arts and Human Sciences, with 2,000 students, is the largest school of those that comprise the University of Neuchâtel. The university has an annual budget of CHF 144 million and an annual research fund of CHF 40 million. Approximately 4,000 students, including 600 PhD students attend the university, and more than 600 diplomas, licences, doctorates and certificates are awarded each year. The university has more than 1,100 employees. History The University of Neuchâtel superseded the Academy, which was created in 1838 by King Frederick William IV of Prussia, Prince of Neuchâtel. It awarded licentiate academic degrees in arts and sciences. In 1848, the Grand Council decreed the closing of the academy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courant Institute Of Mathematical Sciences
The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute and also a mathematics professor at New York University from 1936 to 1972, and serves as a center for research and advanced training in computer science and mathematics. It is located on Gould Plaza next to the New York University Stern School of Business, Stern School of Business and the economics department of the New York University College of Arts & Science, College of Arts and Science. The director of the Courant Institute directly reports to New York University's provost and president and works closely with deans and directors of other NYU colleges and divisions respectively. The undergraduate programs and graduate programs at the Courant Institute are run independently by the institute, and formally associated with the NYU College ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ETH Zurich
ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ranks among Europe's best universities. Like its sister institution École Polytechnique Fédérale de Lausanne, EPFL, ETH Zurich is part of the ETH Domain, Swiss Federal Institutes of Technology Domain, a consortium of universities and research institutes under the Swiss Federal Department of Economic Affairs, Education and Research. , ETH Zurich enrolled 25,380 students from over 120 countries, of which 4,425 were pursuing doctoral degrees. Students, faculty, and researchers affiliated with ETH Zurich include 22 Nobel Prize, Nobel laureates, two Fields Medalists, three Pritzker Architecture Prize, Pritzker Prize winners, and one Turing Award, Turing Award recipient, including Albert Einstein and John von Neumann. It is a founding member o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edinburgh
Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh had a population of in , making it the List of towns and cities in Scotland by population, second-most populous city in Scotland and the List of cities in the United Kingdom, seventh-most populous in the United Kingdom. The Functional urban area, wider metropolitan area had a population of 912,490 in the same year. Recognised as the capital of Scotland since at least the 15th century, Edinburgh is the seat of the Scottish Government, the Scottish Parliament, the Courts of Scotland, highest courts in Scotland, and the Palace of Holyroodhouse, the official residence of the Monarchy of the United Kingdom, British monarch in Scotland. It is also the annual venue of the General Assembly of the Church of Scotland. The city has long been a cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael J
Michael may refer to: People * Michael (given name), a given name * he He ..., a given name * Michael (surname), including a list of people with the surname Michael Given name * Michael (bishop elect)">Michael (surname)">he He ..., a given name * Michael (surname), including a list of people with the surname Michael Given name * Michael (bishop elect), English 13th-century Bishop of Hereford elect * Michael (Khoroshy) (1885–1977), cleric of the Ukrainian Orthodox Church of Canada * Michael Donnellan (fashion designer), Michael Donnellan (1915–1985), Irish-born London fashion designer, often referred to simply as "Michael" * Michael (footballer, born 1982), Brazilian footballer * Michael (footballer, born 1983), Brazilian footballer * Michael (footballer, born 1993), Brazilian footballer * Michael (footballer, born February 1996), Brazilian footballer * Michael (footballer, born March 1996), Brazilian footballer * Michael (footballer, born 1999), Brazilian football ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram, in which any knot can be drawn in many different ways. Therefore, a fundamental p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kervaire–Milnor Group
In mathematics, especially differential topology and cobordism theory, a Kervaire–Milnor group is an abelian group defined as the h-cobordism classes of homotopy spheres with the connected sum as composition and the reverse orientation as inversion. It controls the existence of smooth structures on topological and piecewise linear (PL) manifolds. Concerning the related question of PL structures on topological manifolds, the obstruction is given by the Kirby–Siebenmann invariant, which is a lot easier to understand. In all but three and four dimensions, Kervaire–Milnor groups furthermore give the possible smooth structures on spheres, hence exotic spheres. They are named after the French mathematician Michel Kervaire and the American mathematician John Milnor, who first described them in 1962. (Their paper was originally only supposed to be the first part, but a second part was never published.) Definition An important property of spheres is their neutrality with respect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exotic Sphere
In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold ''M'' that is homeomorphic but not diffeomorphic to the standard Euclidean ''n''-sphere. That is, ''M'' is a sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar one (hence the name "exotic"). The first exotic spheres were constructed by in dimension n = 7 as S^3- bundles over S^4. He showed that there are at least 7 differentiable structures on the 7-sphere. In any dimension showed that the diffeomorphism classes of oriented exotic spheres form the non-trivial elements of an abelian monoid under connected sum, which is a finite abelian group if the dimension is not 4. The classification of exotic spheres by showed that the oriented exotic 7-spheres are the non-trivial elements of a cyclic group of order 28 under the operation of connected sum. These groups are known as Kervaire–Milnor groups. Mo ... [...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 the only mathematician to have won the Fields Medal, the Wolf Prize, the Abel Prize and all three Steele prizes. Early life and career Milnor was born on February 20, 1931, in Orange, New Jersey. His father was J. Willard Milnor, an engineer, 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 Ralph Fox. He remained at Princeton to pursue graduate studies and received his Ph.D. in mathematics in 1954 after completing a doctoral dissertation, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
