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Dieter Kotschick
Dieter Kotschick (born 1963) is a German mathematician, specializing in differential geometry and topology. At age fifteen, Kotschick moved from Transylvania to Germany. He first studied at Heidelberg University and then at the University of Bonn. He received his doctorate from the University of Oxford in 1989 under the supervision of Simon Donaldson with thesis ''On the geometry of certain 4-manifolds'' and held postdoctoral positions at Princeton University and the University of Cambridge. He became a professor at the University of Basel in 1991 and a professor at the Ludwig Maximilian University of Munich in 1998. Kotschick has been a member of the Institute for Advanced Study three times (1989/90, 2008/09 and 2012/13). In 2012 he was elected a Fellow of the American Mathematical Society. In 2009, he solved a 55-year-old open problem posed in 1954 by Friedrich Hirzebruch, which asks "which linear combinations of Chern numbers of smooth complex projective varieties are topologica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transylvania
Transylvania ( ro, Ardeal or ; hu, Erdély; german: Siebenbürgen) is a historical and cultural region in Central Europe, encompassing central Romania. To the east and south its natural border is the Carpathian Mountains, and to the west the Apuseni Mountains. Broader definitions of Transylvania also include the western and northwestern Romanian regions of Crișana and Maramureș, and occasionally Banat. Transylvania is known for the scenery of its Carpathian landscape and its rich history. It also contains Romania's second-largest city, Cluj-Napoca, and other iconic cities and towns such as Brașov, Sibiu, Târgu Mureș, Alba Iulia and Sighișoara. It is also the home of some of Romania's List of World Heritage Sites in Romania, UNESCO World Heritage Sites such as the villages with fortified churches in Transylvania, Villages with fortified churches, the Historic Centre of Sighișoara, the Dacian Fortresses of the Orăștie Mountains and the Rosia Montana Mining Cultural Landsc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pontryagin Number
In mathematics, the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology groups with degrees a multiple of four. Definition Given a real vector bundle ''E'' over ''M'', its ''k''-th Pontryagin class p_k(E) is defined as :p_k(E) = p_k(E, \Z) = (-1)^k c_(E\otimes \Complex) \in H^(M, \Z), where: *c_(E\otimes \Complex) denotes the 2k-th Chern class of the complexification E\otimes \Complex = E\oplus iE of ''E'', *H^(M, \Z) is the 4k-cohomology group of ''M'' with integer coefficients. The rational Pontryagin class p_k(E, \Q) is defined to be the image of p_k(E) in H^(M, \Q), the 4k-cohomology group of ''M'' with rational coefficients. Properties The total Pontryagin class :p(E)=1+p_1(E)+p_2(E)+\cdots\in H^*(M,\Z), is (modulo 2-torsion) multiplicative with respect to Whitney sum of vector bundles, i.e., :2p(E\oplus F)=2p(E)\smile p(F) for two vector bundles ''E'' and ''F'' over ''M'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of The University Of Basel
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 387 BC, established what is known today as the Old Academy. By extension, ''academia'' has come to mean the accumulation, dev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alumni Of The University Of Oxford
Alumni (singular: alumnus (masculine) or alumna (feminine)) are former students of a school, college, or university who have either attended or graduated in some fashion from the institution. The feminine plural alumnae is sometimes used for groups of women. The word is Latin and means "one who is being (or has been) nourished". The term is not synonymous with "graduate"; one can be an alumnus without graduating (Burt Reynolds, alumnus but not graduate of Florida State, is an example). The term is sometimes used to refer to a former employee or member of an organization, contributor, or inmate. Etymology The Latin noun ''alumnus'' means "foster son" or "pupil". It is derived from PIE ''*h₂el-'' (grow, nourish), and it is a variant of the Latin verb ''alere'' "to nourish".Merriam-Webster: alumnus .. Separate, but from the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century German Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inventiones Mathematicae
''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current managing editors are Camillo De Lellis (Institute for Advanced Study, Princeton) and Jean-Benoît Bost (University of Paris-Sud Paris-Sud University (French: ''Université Paris-Sud''), also known as University of Paris — XI (or as Université d'Orsay before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, in ...). Abstracting and indexing The journal is abstracted and indexed in: References External links *{{Official website, https://www.springer.com/journal/222 Mathematics journals Publications established in 1966 English-language journals Springer Science+Business Media academic journals Monthly journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fullerene
A fullerene is an allotrope of carbon whose molecule consists of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to seven atoms. The molecule may be a hollow sphere, ellipsoid, tube, or many other shapes and sizes. Graphene (isolated atomic layers of graphite), which is a flat mesh of regular hexagonal rings, can be seen as an extreme member of the family. Fullerenes with a closed mesh topology are informally denoted by their empirical formula C''n'', often written C''n'', where ''n'' is the number of carbon atoms. However, for some values of ''n'' there may be more than one isomer. The family is named after buckminsterfullerene (C60), the most famous member, which in turn is named after Buckminster Fuller. The closed fullerenes, especially C60, are also informally called buckyballs for their resemblance to the standard ball of association football ("soccer"). Nested closed fullerenes have been named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non- stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles. Regular icosahedra There are two objects, one convex and one nonconvex, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. Both have icosahedral symmetry. The term "regular icosahedron" generally refers to the convex variety, while the nonconvex form is called a ''great icosahedron''. Convex regular icosahedron The convex regular icosahedron is usually referred to simply as the ''regular icosahedron'', one of the five regular Platonic solids, and is represented by its Schläfli symbol , con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soccer Ball
A football (also known as football ball, soccer ball, or association football ball specifically in the United Kingdom) is the ball used in the sport of association football. The name of the ball varies according to whether the sport is called "football", "soccer", or "association football". The ball's spherical shape, as well as its size, weight, and material composition, are specified by Law 2 of the Laws of the Game maintained by the International Football Association Board. Additional, more stringent standards are specified by FIFA and subordinate governing bodies for the balls used in the competitions they sanction. Early footballs began as animal bladders or stomachs that would easily fall apart if kicked too much. Improvements became possible in the 19th century with the introduction of rubber and discoveries of vulcanization by Charles Goodyear. The modern 32-panel ball design was developed in 1962 by Eigil Nielsen, and technological research continues to develop footba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adidas Telstar
Telstar is a football made by Adidas. The iconic 32-panel alternating black-and-white design of the ball, based on the work of Eigil Nielsen, has since become a global standard design used to portray a football in different media. Ball The ball was first introduced as the "Telstar Elast" for the 1968 European Football Championship. A slightly different ball named "Telstar" was used as the official match ball of the 1970 FIFA World Cup in Mexico. The similar "Telstar Durlast" was one of two official balls, along with the ''Chile Durlast'', of the 1974 FIFA World Cup held in West Germany. The ball was also used in the 1972 and 1976 European Championships. The Telstar was the first World Cup ball to use the now-familiar truncated icosahedron for its design, consisting of 12 black pentagonal and 20 white hexagonal panels. The 32-panel configuration had been introduced in 1962 by Select Sport, and was also used in the official logo for the 1970 World Cup. The black-and-white pat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
