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Dennis Sullivan (other)
Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the Graduate Center of the City University of New York and is a distinguished professor at Stony Brook University. Sullivan was awarded the Wolf Prize in Mathematics in 2010 and the Abel Prize in 2022. Early life and education Sullivan was born in Port Huron, Michigan, on February 12, 1941.. His family moved to Houston soon afterwards. He entered Rice University to study chemical engineering but switched his major to mathematics in his second year after encountering a particularly motivating mathematical theorem. The change was prompted by a special case of the uniformization theorem, according to which, in his own words: He received his Bachelor of Arts degree from Rice University in 1963. He obtained his Doctor of Philosophy from Princeton University in 1966 with his thesis, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Port Huron, Michigan
Port Huron is a city in and seat of government of St. Clair County, Michigan, United States. The population was 28,983 at the 2020 census. The city is bordered on the west by Port Huron Township, but the two are administered autonomously. Port Huron is located along the source of the St. Clair River at the southern end of Lake Huron. The city is along the Canada–United States border and directly across the river from Sarnia, Ontario. The two cities are connected by the Blue Water Bridge at the eastern terminus of Interstate 69/ Interstate 94. Port Huron has the easternmost point of land in the state of Michigan and is also one of the northernmost areas included in the Detroit–Warren–Dearborn Metropolitan Statistical Area ( Metro Detroit). History This area was long occupied by the Ojibwa people. French colonists had a temporary trading post and fort at this site in the 17th century. In 1814, following the War of 1812, the United States established Fort Gratiot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Localization Of A Topological Space
In mathematics, well-behaved topological spaces can be localized at primes, in a similar way to the localization of a ring at a prime. This construction was described by Dennis Sullivan in 1970 lecture notes that were finally published in . The reason to do this was in line with an idea of making topology, more precisely algebraic topology, more geometric. Localization of a space ''X'' is a geometric form of the algebraic device of choosing 'coefficients' in order to simplify the algebra, in a given problem. Instead of that, the localization can be applied to the space ''X'', directly, giving a second space ''Y''. Definitions We let ''A'' be a subring of the rational numbers, and let ''X'' be a simply connected CW complex. Then there is a simply connected CW complex ''Y'' together with a map from ''X'' to ''Y'' such that *''Y'' is ''A''-local; this means that all its homology groups are modules over ''A'' *The map from ''X'' to ''Y'' is universal for (homotopy classes of) maps from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graduate Center Of The City University Of New York
The Graduate School and University Center of the City University of New York (CUNY Graduate Center) is a public research institution and postgraduate university in New York City. Formed in 1961 as Division of Graduate Studies at City University of New York, it was renamed to Graduate School and University Center in 1969. Serving as the principal doctorate-granting institution of the City University of New York (CUNY) system, CUNY Graduate Center is classified among " R1: Doctoral Universities – Very High Research Activity". CUNY Graduate Center is located at the B. Altman and Company Building at 365 Fifth Avenue in Midtown Manhattan. It offers 32 doctoral programs, 18 master's programs, and operates over 30 research centers and institutes. The Graduate Center employs a core faculty of approximately 130, in addition to over 1,700 faculty members appointed from other CUNY campuses throughout New York City. As of fall 2025, the Graduate Center enrolls over 3,100 students, of whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, 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 number, 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 (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Topology
In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originated in the 1935 classification of lens spaces by Reidemeister torsion, which required distinguishing spaces that are homotopy equivalent but not homeomorphic. This was the origin of simple homotopy, ''simple'' homotopy theory. The use of the term geometric topology to describe these seems to have originated rather recently. Differences between low-dimensional and high-dimensional topology Manifolds differ radically in behavior in high and low dimension. High-dimensional topology refers to manifolds of dimension 5 and above, or in relative terms, embeddings in codimension 3 and above. Low-dimensional topology is concerned with questions in dimensions up to 4, or embeddings in codimension up to 2. Dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up to homeomorphism, though usually most classify up to Homotopy#Homotopy equivalence and null-homotopy, homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Main branches Below are some of the main areas studied in algebraic topology: Homotopy groups In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy groups record information ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balzan Prize
The International Balzan Prize Foundation awards four annual monetary prizes to people or organizations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the brotherhood of man. History The assets behind the foundation were established by the Italian Eugenio Balzan (1874–1953), a part-owner of who had invested his assets in Switzerland and in 1933 had left Italy in protest against fascism. He left a substantial inheritance to his daughter Angela Lina Balzan (1892–1956), who at the time was suffering an incurable disease. Before her death, she left instructions for the foundation and since then it has two headquarters, the Prize administered from Milan, the Fund from Zurich. The first award was in fact one million Swiss francs to the Nobel Foundation in 1961. After 1962, a gap of 16 years followed when prizes recommenced with an award of half a million Swiss francs to Mother Teresa. Award ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf Prize In Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. The Wolf Prize includes a monetary award of $100,000. According to a reputation survey conducted in 2013 and 2014, the Wolf Prize in Mathematics is the third most prestigious international academic award in mathematics, after the Abel Prize and the Fields Medal. Laureates Laureates per country Below is a chart of all laureates per country (updated to 2024 laureates). Some laureates are counted more than once if they have multiple citizenships. Notes See also * List of mathematics awards References External links * * * Israel-Wolf-Prizes 2015Jerusalempost Wolf Prizes 2017Jerusalempost Wolf Prizes 2018Wolf Prize 2019 {{DEFAULTSORT:Wolf Prize In Mathematics Mathematics Mathematics is a field of study th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Medal Of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral science, behavioral and social sciences, biology, chemistry, engineering, mathematics and physics. The twelve member presidential Committee on the National Medal of Science is responsible for selecting award recipients and is administered by the National Science Foundation (NSF). It is the highest science award in the United States. History The National Medal of Science was established on August 25, 1959, by an act of the Congress of the United States under . The medal was originally to honor scientists in the fields of the "physical, biological, mathematical, or engineering sciences". The Committee on the National Medal of Science was established on August 23, 1961, by Executive order (United States), executive order 10961 of President John F. Kennedy. O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oswald Veblen Prize In Geometry
__NOTOC__ The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was funded in 1961 in memory of Oswald Veblen and first issued in 1964. The Veblen Prize is now worth US$5000, and is awarded every three years. The first seven prize winners were awarded for works in topology. James Harris Simons and William Thurston were the first ones to receive it for works in geometry. As of 2022, there have been thirty-seven prize recipients. List of recipients * 1964 Christos Papakyriakopoulos, for: ::"On Solid Tori", ''Proceedings of the London Mathematical Society'' ::"On Dehn's lemma and the asphericity of knots", ''Annals of Mathematics'' * 1964 Raoul Bott, for: ::"The space of loops on a Lie group", ''Michigan Math. J.'' ::"The stable homotopy of the classical groups", ''Annals of Mathematics'' * 1966 Stephen Smale * 1966 Morton Brown and Barry Mazur * 1971 Robion Kirby, for: ::"Stable homeomorphis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
