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Karen Uhlenbeck
Karen Keskulla Uhlenbeck (born August 24, 1942) is an American mathematician and one of the founders of modern geometric analysis. She is a professor emeritus of mathematics at the University of Texas at Austin, where she held the Sid W. Richardson Foundation Regents Chair. She is currently a distinguished visiting professor at the Institute for Advanced Study and a visiting senior research scholar at Princeton University. Uhlenbeck was elected to the American Philosophical Society in 2007. She won the 2019 Abel Prize for "her pioneering achievements in geometric partial differential equations, gauge theory, and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics." She is the first, and so far only, woman to win the prize since its inception in 2003. She donated half of the prize money to organizations which promote more engagement of women in research mathematics. Life and career Uhlenbeck was born in Cleveland, Ohio, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cleveland
Cleveland ( ), officially the City of Cleveland, is a city in the U.S. state of Ohio and the county seat of Cuyahoga County. Located in the northeastern part of the state, it is situated along the southern shore of Lake Erie, across the U.S. maritime border with Canada, northeast of Cincinnati, northeast of Columbus, and approximately west of Pennsylvania. The largest city on Lake Erie and one of the major cities of the Great Lakes region, Cleveland ranks as the 54th-largest city in the U.S. with a 2020 population of 372,624. The city anchors both the Greater Cleveland metropolitan statistical area (MSA) and the larger Cleveland–Akron–Canton combined statistical area (CSA). The CSA is the most populous in Ohio and the 17th largest in the country, with a population of 3.63 million in 2020, while the MSA ranks as 34th largest at 2.09 million. Cleveland was founded in 1796 near the mouth of the Cuyahoga River by General Moses Cleaveland, after whom the city was named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Texas At Austin
The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 graduate students and 3,133 teaching faculty as of Fall 2021, it is also the largest institution in the system. It is ranked among the top universities in the world by major college and university rankings, and admission to its programs is considered highly selective. UT Austin is considered one of the United States's Public Ivies. The university is a major center for academic research, with research expenditures totaling $679.8 million for fiscal year 2018. It joined the Association of American Universities in 1929. The university houses seven museums and seventeen libraries, including the LBJ Presidential Library and the Blanton Museum of Art, and operates various auxiliary research facilities, such as the J. J. Pickle Research Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrable System
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, such that its behaviour has far fewer degrees of freedom than the dimensionality of its phase space; that is, its evolution is restricted to a submanifold within its phase space. Three features are often referred to as characterizing integrable systems: * the existence of a ''maximal'' set of conserved quantities (the usual defining property of complete integrability) * the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) * the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability) Integrable systems may be seen as very different in qualitative character from mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Theory
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the ''symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called '' gauge bosons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and community outreach. Considered the first learned society in the United States, it has about 1,000 elected members, and by April 2020 had had only 5,710 members since its creation. Through research grants, published journals, the American Philosophical Society Museum, an extensive library, and regular meetings, the society supports a variety of disciplines in the humanities and the sciences. Philosophical Hall, now a museum, is just east of Independence Hall in Independence National Historical Park; it was designated a National Historic Landmark in 1965. History The Philosophical Society, as it was originally called, was founded in 1743 by Benjamin Franklin, James Alexander (lawyer), James Alexander, Francis Hopkinson, John Bartram, Philip Syn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the highest-ranked universities in the world. The institution moved to Newark, New Jersey, Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Agnes Scott College
Agnes Scott College is a private women's liberal arts college in Decatur, Georgia. The college enrolls approximately 1,000 undergraduate and graduate students. The college is affiliated with the Presbyterian Church and is considered one of the Seven Sisters of the South. It also offers co-educational graduate programs. History The college was founded in 1889 as Decatur Female Seminary by Presbyterian minister Frank Henry Gaines. In 1890, the name was changed to Agnes Scott Institute to honor the mother of the college's primary benefactor, Col. George Washington Scott. The name was changed again to Agnes Scott College in 1906, and remains today a women's college. Agnes Scott is considered the first higher education institution in the state of Georgia to receive regional accreditation. The ninth and current president since July 2018 is Leocadia I. Zak, who previously worked as director of the U.S. Trade and Development Agency (USTDA). On July 27, 1994, the campus was listed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Analysis
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck,Jackson, Allyn. (2019)Founder of geometric anal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shing-Tung Yau
Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathematics at Tsinghua University. Yau was born in Shantou, China, moved to Hong Kong at a young age, and to the United States in 1969. He was awarded the Fields Medal in 1982, in recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors to the development of modern differential geometry and geometric analysis. The impact of Yau's work can be seen in the mathematical and physical fields of differential geometry, partial differential equations, convex geometry, algebraic geometry, enumerative geometry, mirror symmetry, general relativity, and string theory, while his work has also touched upon applied ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Palais
Richard Sheldon Palais (born May 22, 1931) is a mathematician working in geometry who introduced the principle of symmetric criticality, the Mostow–Palais theorem, the Lie–Palais theorem, the Morse–Palais lemma, and the Palais–Smale compactness condition. From 1965 to 1967 Palais was a Sloan Research Fellowship, Sloan Fellow. In 1970 he was an invited speaker (''Banach manifolds of fiber bundle sections'') at the International Congress of Mathematicians in Nice. From 1965 to 1982 he was an editor for the ''Journal of Differential Geometry'' and from 1966 to 1969 an editor for the ''Transactions of the American Mathematical Society''. In 2010 he received a Lester R. Ford Award. In 2012 he became a fellow of the American Mathematical Society. retrieved 2013-05- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
