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Tobias Colding
Tobias Holck Colding (born 1963) is a Danish mathematician working on geometric analysis, and low-dimensional topology. He is the great grandchild of Ludwig August Colding. Biography He was born in Copenhagen, Denmark, to Torben Holck Colding and Benedicte Holck Colding. He received his Ph.D. in mathematics in 1992 at the University of Pennsylvania under Chris Croke. Since 2005 Colding has been a professor of mathematics at MIT. He was on the faculty at the Courant Institute of New York University in various positions from 1992 to 2008. He has also been a visiting professor at MIT (2000–01) and at Princeton University (2001–02) and a postdoctoral fellow at MSRI (1993–94). Colding lives in Cambridge, MA, with his wife and three children. Work In the early stage of his career, Colding did impressive work on manifolds with bounds on Ricci curvature. In 1995 he presented this work at the Geometry Festival. He began working with Jeff Cheeger while at NYU. He ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Copenhagen
Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan area has 2,057,142 people. Copenhagen is on the islands of Zealand and Amager, separated from Malmö, Sweden, by the Øresund strait. The Øresund Bridge connects the two cities by rail and road. Originally a Viking fishing village established in the 10th century in the vicinity of what is now Gammel Strand, Copenhagen became the capital of Denmark in the early 15th century. Beginning in the 17th century, it consolidated its position as a regional centre of power with its institutions, defences, and armed forces. During the Renaissance the city served as the de facto capital of the Kalmar Union, being the seat of monarchy, governing the majority of the present day Nordic region in a personal union with Sweden and Norway ruled by the Danis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ricci Curvature
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space. The Ricci tensor can be characterized by measurement of how a shape is deformed as one moves along geodesics in the space. In general relativity, which involves the pseudo-Riemannian setting, this is reflected by the presence of the Ricci tensor in the Raychaudhuri equation. Partly for this reason, the Einstein field equations propose that spacetime can be described by a pseudo-Riemannian metric, with a strikingly simple relationship between the Ricci tensor and the matter content of the universe. Like the metric tensor, the Ricci tensor assigns to each tangent space of the manifold a symmetric bili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Georgia
, mottoeng = "To teach, to serve, and to inquire into the nature of things.""To serve" was later added to the motto without changing the seal; the Latin motto directly translates as "To teach and to inquire into the nature of things." , established = , endowment = $1.8 billion (2021)As of June 30, 2021. , type = Public flagship land-grant research university , parent = University System of Georgia , accreditation = SACS , academic_affiliation = , president = Jere W. Morehead , provost = S. Jack Hu , city = Athens , state=Georgia , country = United States , coordinates = , faculty = 3,119 , students = 40,118 (fall 2021) , undergrad = 30,166 (fall 2021) , postgrad = 9,952 (fall 2021) , free_label2 = Newspaper , free2 = '' The Red & Black'' , campus = Midsize city / College town , campus_size = (main campus) (total) , colors = , sports_nickname = Bulldogs , sporting_affiliations = NCAA Division I FBS – SEC , mascot = Uga X (live English Bulldo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Cambridge
, mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Scholars of the University of Cambridge , type = Public research university , endowment = £7.121 billion (including colleges) , budget = £2.308 billion (excluding colleges) , chancellor = The Lord Sainsbury of Turville , vice_chancellor = Anthony Freeling , students = 24,450 (2020) , undergrad = 12,850 (2020) , postgrad = 11,600 (2020) , city = Cambridge , country = England , campus_type = , sporting_affiliations = The Sporting Blue , colours = Cambridge Blue , website = , logo = University of Cambridge logo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odense
Odense ( , , ) is the third largest city in Denmark (behind Copenhagen and Aarhus) and the largest city on the island of Funen. As of 1 January 2022, the city proper had a population of 180,863 while Odense Municipality had a population of 205,978, making it the fourth largest municipality in Denmark (behind Copenhagen, Aarhus and Aalborg municipalities). Eurostat and OECD have used a definition for the Metropolitan area of Odense (referred to as a ''Functional urban area''), which includes all municipalities in the Province (Danish: Provinces of Denmark, ''landsdel'') of Funen (Danish: ''Fyn''), with a total population of 504,066 as of 1 July 2022https://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=urb_lpop1&lang=en&fbclid=IwAR2SFTy1xGM8VcLHijhmSDQWd9Fr3TYx7JlKxg81_09e-KzEtmEgjL5L2UU By road, Odense is located north of Svendborg, to the south of Aarhus and to the southwest of Copenhagen. The city was the seat of Odense County until 1970, and Funen County from 1970 unt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Tennessee
The University of Tennessee (officially The University of Tennessee, Knoxville; or UT Knoxville; UTK; or UT) is a public land-grant research university in Knoxville, Tennessee. Founded in 1794, two years before Tennessee became the 16th state, it is the flagship campus of the University of Tennessee system, with ten undergraduate colleges and eleven graduate colleges. It hosts more than 30,000 students from all 50 states and more than 100 foreign countries. It is classified among "R1: Doctoral Universities – Very high research activity". UT's ties to nearby Oak Ridge National Laboratory, established under UT President Andrew Holt and continued under the UT–Battelle partnership, allow for considerable research opportunities for faculty and students. Also affiliated with the university are the Howard H. Baker Jr. Center for Public Policy, the University of Tennessee Anthropological Research Facility, and the University of Tennessee Arboretum, which occupies of nearby Oak R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Curvature Flow
In the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space). Intuitively, a family of surfaces evolves under mean curvature flow if the normal component of the velocity of which a point on the surface moves is given by the mean curvature of the surface. For example, a round sphere evolves under mean curvature flow by shrinking inward uniformly (since the mean curvature vector of a sphere points inward). Except in special cases, the mean curvature flow develops singularities. Under the constraint that volume enclosed is constant, this is called surface tension flow. It is a parabolic partial differential equation, and can be interpreted as "smoothing". Existence and uniqueness The following was shown by Michael Gage and Richard S. Hamilton as an application of Hamilton's general existence theorem for parabolic geometric f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Surfaces
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum. Definitions Minimal surfaces can be defined in several equivalent ways in R3. The fact that they are equivalent serves to demonstrate how minimal surface theory lies at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Functions
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that is, : \frac + \frac + \cdots + \frac = 0 everywhere on . This is usually written as : \nabla^2 f = 0 or :\Delta f = 0 Etymology of the term "harmonic" The descriptor "harmonic" in the name harmonic function originates from a point on a taut string which is undergoing harmonic motion. The solution to the differential equation for this type of motion can be written in terms of sines and cosines, functions which are thus referred to as ''harmonics''. Fourier analysis involves expanding functions on the unit circle in terms of a series of these harmonics. Considering higher dimensional analogues of the harmonics on the unit ''n''-sphere, one arrives at the spherical harmonics. These functions satisfy Laplace's equation and over time "harmonic" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Minicozzi II
William Philip Minicozzi II is an American mathematician. He was born in Bryn Mawr, Pennsylvania, in 1967. Career Minicozzi graduated from Princeton University in 1990 and received his Ph.D. from Stanford University in 1994 under the direction of Richard Schoen. After graduating he spent a year at the Courant Institute of New York University as a visiting member where he began working with Tobias Colding on harmonic functions on Riemannian manifolds, work he was later invited to present at the Geometry Festival. In 1995, he went to the Johns Hopkins University, with a National Science Foundation postdoctoral fellowship. Minicozzi became the J. J. Sylvester Professor of Mathematics at Johns Hopkins in 2002, and later became Krieger-Eisenhower Professor there. He turned to work on minimal surfaces, continuing to work with Tobias Colding. In 2012 he joined MIT as a professor of mathematics. Currently, they mainly work on the mean curvature flow. In addition to his teaching and res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
