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Joan Birman
Joan Sylvia Lyttle Birman (born May 30, 1927, in New York CityLarry Riddle., ''Biographies of Women Mathematicians'', at Agnes Scott College) is an American mathematician, specializing in low-dimensional topology. She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is research professor emerita at Barnard College, Columbia University, where she has been since 1973. Family Her parents were George and Lillian Lyttle, both Jewish immigrants. Her father was from Russia but grew up in Liverpool, England. Her mother was born in New York and her parents were Russian-Polish immigrants. At age 17, George emigrated to the US and became a successful dress manufacturer. He appreciated the opportunities from having a business but he wanted his daughters to focus on education. She has three children, Kenneth P. Birman, Deborah Birman Shlider, and Carl David Birman. Her lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the United States, and is more than twice as populous as second-place Los Angeles. New York City lies at the southern tip of New York State, and constitutes the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the world by urban landmass. With over 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York is one of the world's most populous megacities, and over 58 million people live within of the city. New York City is a global cultural, financial, entertainment, and media center with a significant influence on commerce, health care and life sciences, research, technology, education, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In the mathematical field of topology, knot theory is the study of 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 (in topology, a circle is not bound to the classical geometric concept, but to all of its homeomorphisms). 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 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 d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mapping Class Group Of A Surface
In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up to continuous (in the compact-open topology) deformation. It is of fundamental importance for the study of 3-manifolds via their embedded surfaces and is also studied in algebraic geometry in relation to moduli problems for curves. The mapping class group can be defined for arbitrary manifolds (indeed, for arbitrary topological spaces) but the 2-dimensional setting is the most studied in group theory. The mapping class group of surfaces are related to various other groups, in particular braid groups and outer automorphism groups. History The mapping class group appeared in the first half of the twentieth century. Its origins lie in the study of the topology of hyperbolic surfaces, and especially in the study of the intersections of closed curves on these surfaces. The earl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stevens Institute Of Technology
Stevens Institute of Technology is a private research university in Hoboken, New Jersey. Founded in 1870, it is one of the oldest technological universities in the United States and was the first college in America solely dedicated to mechanical engineering. The 55-acre campus encompasses Castle Point, the highest point in Hoboken, a campus green and 43 academic, student and administrative buildings. Established through an 1868 bequest from Edwin Augustus Stevens, enrollment at Stevens includes more than 8,000 undergraduate and graduate students representing 47 states and 60 countries throughout Asia, Europe and Latin America. Stevens comprises three schools and one college that deliver technology-based STEM (science, technology, engineering and mathematics) degrees and degrees in business, arts, humanities and social sciences: The Charles V. Schaefer, Jr., School of Engineering and Science, School of Business, School of Systems and Enterprises, and College of Arts and Letters. F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Human Rights
Human rights are moral principles or normsJames Nickel, with assistance from Thomas Pogge, M.B.E. Smith, and Leif Wenar, 13 December 2013, Stanford Encyclopedia of PhilosophyHuman Rights Retrieved 14 August 2014 for certain standards of human behaviour and are regularly protected in municipal and international law. They are commonly understood as inalienable,The United Nations, Office of the High Commissioner of Human RightsWhat are human rights? Retrieved 14 August 2014 fundamental rights "to which a person is inherently entitled simply because she or he is a human being" and which are "inherent in all human beings",Burns H. Weston, 20 March 2014, Encyclopædia Britannicahuman rights Retrieved 14 August 2014. regardless of their age, ethnic origin, location, language, religion, ethnicity, or any other status. They are applicable everywhere and at every time in the sense of being universal, and they are egalitarian in the sense of being the same for everyone. They are reg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Birman
Joseph Leon Birman (May 21, 1927 in New York City – October 1, 2016 in New Rochelle) was an American theoretical solid-state physicist. Life Birman was the son of a salesman. He went to the Bronx High School of Science (graduated in 1943) then studied at City College of New York, graduating with a bachelor's degree in 1947. He next attended Columbia University, gaining a master's degree in 1950 and a PhD in theoretical chemistry in 1952. He then spent about ten years at an electronics and telecommunications research lab (later GTE Research Labs in Queens) in New York where he studied the optical properties of semiconductors. From 1962 he was a professor at New York University and from 1974 professor at the City College of New York. Most recently, he was Distinguished Professor at CUNY. From 1969 to 1970 he was a guest professor in Paris. In 1974 he became received an honorary doctorate from the University of Rennes. He was a Guggenheim Fellow, Lady Davis Fellow at the Techni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
England
England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain, which lies in the North Atlantic, and includes over 100 smaller islands, such as the Isles of Scilly and the Isle of Wight. The area now called England was first inhabited by modern humans during the Upper Paleolithic period, but takes its name from the Angles, a Germanic tribe deriving its name from the Anglia peninsula, who settled during the 5th and 6th centuries. England became a unified state in the 10th century and has had a significant cultural and legal impact on the wider world since the Age of Discovery, which began during the 15th century. The English language, the Anglican Church, and Engli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liverpool
Liverpool is a city and metropolitan borough in Merseyside, England. With a population of in 2019, it is the 10th largest English district by population and its metropolitan area is the fifth largest in the United Kingdom, with a population of 2.24 million. On the eastern side of the Mersey Estuary, Liverpool historically lay within the ancient hundred of West Derby in the county of Lancashire. It became a borough in 1207, a city in 1880, and a county borough independent of the newly-created Lancashire County Council in 1889. Its growth as a major port was paralleled by the expansion of the city throughout the Industrial Revolution. Along with general cargo, freight, and raw materials such as coal and cotton, merchants were involved in the slave trade. In the 19th century, Liverpool was a major port of departure for English and Irish emigrants to North America. It was also home to both the Cunard and White Star Lines, and was the port of registry of the ocean lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Immigrants
Immigration is the international movement of people to a destination country of which they are not natives or where they do not possess citizenship in order to settle as permanent residents or naturalized citizens. Commuters, tourists, and other short-term stays in a destination country do not fall under the definition of immigration or migration; seasonal labour immigration is sometimes included, however. As for economic effects, research suggests that migration is beneficial both to the receiving and sending countries. Research, with few exceptions, finds that immigration on average has positive economic effects on the native population, but is mixed as to whether low-skilled immigration adversely affects low-skilled natives. Studies show that the elimination of barriers to migration would have profound effects on world GDP, with estimates of gains ranging between 67 and 147 percent for the scenarios in which 37 to 53 percent of the developing countries' workers migra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The people of the Kingdom of Israel and the ethnic and religious group known as the Jewish people that descended from them have been subjected to a number of forced migrations in their history" and Hebrews of historical Israel and Judah. Jewish ethnicity, nationhood, and religion are strongly interrelated, "Historically, the religious and ethnic dimensions of Jewish identity have been closely interwoven. In fact, so closely bound are they, that the traditional Jewish lexicon hardly distinguishes between the two concepts. Jewish religious practice, by definition, was observed exclusively by the Jewish people, and notions of Jewish peoplehood, nation, and community were suffused with faith in the Jewish God, the practice of Jewish (religious) la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Geometry
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently, such a distribution may be given (at least locally) as the kernel of a differential one-form, and the non-integrability condition translates into a maximal non-degeneracy condition on the form. These conditions are opposite to two equivalent conditions for ' complete integrability' of a hyperplane distribution, i.e. that it be tangent to a codimension one foliation on the manifold, whose equivalence is the content of the Frobenius theorem. Contact geometry is in many ways an odd-dimensional counterpart of symplectic geometry, a structure on certain even-dimensional manifolds. Both contact and symplectic geometry are motivated by the mathematical formalism of classical mechanics, where one can consider either the even-dimensional phase space of a mechanical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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