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Hermann Schubert
__NOTOC__ Hermann Cäsar Hannibal Schubert (22 May 1848 – 20 July 1911) was a German mathematician. Schubert was one of the leading developers of enumerative geometry, which considers those parts of algebraic geometry that involve a finite number of solutions. In 1874, Schubert won a prize for solving a question posed by Zeuthen. Schubert calculus was named after him. Schubert tutored Adolf Hurwitz at the Realgymnasium Andreanum in Hildesheim, Hanover, and arranged for Hurwitz to study under Felix Klein at University. See also * Schubert cycle or Schubert variety * Schubert polynomial In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties. They were introduced by and are named after Hermann Schubert. Background described the history ... Publications * References *Werner Burau and Bodo Renschuch, "Ergänzungen zur Biographie von Hermann Schubert," (Complements to the biogra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potsdam
Potsdam () is the capital and, with around 183,000 inhabitants, largest city of the German state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the River Havel, a tributary of the Elbe, downstream of Berlin, and lies embedded in a hilly morainic landscape dotted with many lakes, around 20 of which are located within Potsdam's city limits. It lies some southwest of Berlin's city centre. The name of the city and of many of its boroughs are of Slavic origin. Potsdam was a residence of the Prussian kings and the German Kaiser until 1918. Its planning embodied ideas of the Age of Enlightenment: through a careful balance of architecture and landscape, Potsdam was intended as "a picturesque, pastoral dream" which would remind its residents of their relationship with nature and reason. The city, which is over 1000 years old, is widely known for its palaces, its lakes, and its overall historical and cultural significance. Landmarks include ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hieronymus Georg Zeuthen
Hieronymus Georg Zeuthen (15 February 1839 – 6 January 1920) was a Danish mathematician. He is known for work on the enumerative geometry of conic sections, algebraic surfaces, and history of mathematics. Biography Zeuthen was born in Grimstrup near Varde where his father was a minister. In 1849, his father moved to a church in Sorø where Zeuthen began his secondary schooling. In 1857 he entered the University of Copenhagen to study mathematics and graduated with a master's degree in 1862. Following this he earned a scholarship to study abroad, and decided to visit Paris where he studied geometry with Michel Chasles. After returning to Copenhagen, Zeuthen submitted his doctoral dissertation on a new method to determine the characteristics of conic systems in 1865. Enumerative geometry remained his focus up until 1875. In 1871 he was appointed as an extraordinary professor at the University of Copenhagen, as well as becoming an editor of ''Matematisk Tidsskrift'', a position ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Mathematicians
The 19th (nineteenth) century began on 1 January 1801 ( MDCCCI), and ended on 31 December 1900 ( MCM). The 19th century was the ninth century of the 2nd millennium. The 19th century was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanding beyond its British homeland for the first time during this century, particularly remaking the economies and societies of the Low Countries, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Islamic gunpowder empires fell into decline and European imperialism brought much of South Asia, Southeast Asia, and almost all of Africa under colonial rule. It was also marked by the collapse of the large S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1911 Deaths
A notable ongoing event was the Comparison of the Amundsen and Scott Expeditions, race for the South Pole. Events January * January 1 – A decade after federation, the Northern Territory and the Australian Capital Territory are added to the Commonwealth of Australia. * January 3 ** 1911 Kebin earthquake: An earthquake of 7.7 Moment magnitude scale, moment magnitude strikes near Almaty in Russian Turkestan, killing 450 or more people. ** Siege of Sidney Street in London: Two Latvian people, Latvian anarchists die, after a seven-hour siege against a combined police and military force. Home Secretary Winston Churchill arrives to oversee events. * January 5 – Egypt's Zamalek SC is founded as a general sports and Association football club by Belgian lawyer George Merzbach as Qasr El Nile Club. * January 14 – Roald Amundsen's South Pole expedition makes landfall, on the eastern edge of the Ross Ice Shelf. * January 18 – Eugene B. El ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1848 Births
1848 is historically famous for the wave of revolutions, a series of widespread struggles for more liberal governments, which broke out from Brazil to Hungary; although most failed in their immediate aims, they significantly altered the political and philosophical landscape and had major ramifications throughout the rest of the century. Ereignisblatt aus den revolutionären Märztagen 18.-19. März 1848 mit einer Barrikadenszene aus der Breiten Strasse, Berlin 01.jpg, Cheering revolutionaries in Berlin, on March 19, 1848, with the new flag of Germany Lar9 philippo 001z.jpg, French Revolution of 1848: Republican riots forced King Louis-Philippe to abdicate Zeitgenössige Lithografie der Nationalversammlung in der Paulskirche.jpg, German National Assembly's meeting in St. Paul's Church Pákozdi csata.jpg, Battle of Pákozd in the Hungarian Revolution of 1848 Events January–March * January 3 – Joseph Jenkins Roberts is sworn in, as the first president of the inde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schubert Polynomial
In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties. They were introduced by and are named after Hermann Schubert. Background described the history of Schubert polynomials. The Schubert polynomials \mathfrak_w are polynomials in the variables x_1,x_2,\ldots depending on an element w of the infinite symmetric group S_\infty of all permutations of \N fixing all but a finite number of elements. They form a basis for the polynomial ring \Z _1,x_2,\ldots/math> in infinitely many variables. The cohomology of the flag manifold \text(m) is \Z _1, x_2,\ldots, x_mI, where I is the ideal generated by homogeneous symmetric functions of positive degree. The Schubert polynomial \mathfrak_w is the unique homogeneous polynomial of degree \ell(w) representing the Schubert cycle of w in the cohomology of the flag manifold \text(m) for all sufficiently large m. Properties *If w_0 is the permutation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schubert Variety
In algebraic geometry, a Schubert variety is a certain subvariety of a Grassmannian, usually with singular points. Like a Grassmannian, it is a kind of moduli space, whose points correspond to certain kinds of subspaces ''V'', specified using linear algebra, inside a fixed vector subspace ''W''. Here ''W'' may be a vector space over an arbitrary field, though most commonly over the complex numbers. A typical example is the set ''X'' whose points correspond to those 2-dimensional subspaces ''V'' of a 4-dimensional vector space ''W'', such that ''V'' non-trivially intersects a fixed (reference) 2-dimensional subspace ''W''2: :X \ =\ \. Over the real number field, this can be pictured in usual ''xyz''-space as follows. Replacing subspaces with their corresponding projective spaces, and intersecting with an affine coordinate patch of \mathbb(W), we obtain an open subset ''X''° ⊂ ''X''. This is isomorphic to the set of all lines ''L'' (not necessarily through the origin) which m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felix Klein
Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory. His 1872 Erlangen program, classifying geometries by their basic symmetry groups, was an influential synthesis of much of the mathematics of the time. Life Felix Klein was born on 25 April 1849 in Düsseldorf, to Prussian parents. His father, Caspar Klein (1809–1889), was a Prussian government official's secretary stationed in the Rhine Province. His mother was Sophie Elise Klein (1819–1890, née Kayser). He attended the Gymnasium in Düsseldorf, then studied mathematics and physics at the University of Bonn, 1865–1866, intending to become a physicist. At that time, Julius Plücker had Bonn's professorship of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker's interest wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hanover
Hanover (; german: Hannover ; nds, Hannober) is the capital and largest city of the German state of Lower Saxony. Its 535,932 (2021) inhabitants make it the 13th-largest city in Germany as well as the fourth-largest city in Northern Germany after Berlin, Hamburg and Bremen. Hanover's urban area comprises the towns of Garbsen, Langenhagen and Laatzen and has a population of about 791,000 (2018). The Hanover Region has approximately 1.16 million inhabitants (2019). The city lies at the confluence of the River Leine and its tributary the Ihme, in the south of the North German Plain, and is the largest city in the Hannover–Braunschweig–Göttingen–Wolfsburg Metropolitan Region. It is the fifth-largest city in the Low German dialect area after Hamburg, Dortmund, Essen and Bremen. Before it became the capital of Lower Saxony in 1946, Hannover was the capital of the Principality of Calenberg (1636–1692), the Electorate of Hanover (1692–1814), the Kingdom of Hannover ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hildesheim
Hildesheim (; nds, Hilmessen, Hilmssen; la, Hildesia) is a city in Lower Saxony, Germany with 101,693 inhabitants. It is in the district of Hildesheim, about southeast of Hanover on the banks of the Innerste River, a small tributary of the Leine River. The Holy Roman Emperor Louis the Pious founded the Bishopric of Hildesheim in 815 and created the first settlement with a chapel on the so called ''Domhügel''. Hildesheim is situated on autobahn route 7, and hence is at the connection point of the North (Hamburg and beyond) with the South of Europe. With the Hildesheim Cathedral and the St. Michael's Church, Hildesheim became a UNESCO World Heritage Site in 1985. In 2015 the city and the diocese celebrated their 1200th anniversary. History Early years According to tradition, the city was named after its notorious founder ''Hildwin.'' The city is one of the oldest cities in Northern Germany, became the seat of the Bishopric of Hildesheim in 815 and may have been f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Hurwitz
Adolf Hurwitz (; 26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory. Early life He was born in Hildesheim, then part of the Kingdom of Hanover, to a Jewish family and died in Zürich, in Switzerland. His father Salomon Hurwitz, a merchant, was not wealthy. Hurwitz's mother, Elise Wertheimer, died when he was three years old. Family records indicate that he had siblings and cousins, but their names have yet to be confirmed except for an older brother, Julius, with whom he developed an arithmetical theory for complex continued fractions circa 1890. Hurwitz entered the in Hildesheim in 1868. He was taught mathematics there by Hermann Schubert. Schubert persuaded Hurwitz's father to allow him to attend university, and arranged for Hurwitz to study with Felix Klein at Munich. Salomon Hurwitz could not afford to send his son to university, but his friend, Mr. Edwards, assisted financially. Educational career Hur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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