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Simon Donaldson
Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London. Biography Donaldson's father was an electrical engineer in the physiology department at the University of Cambridge, and his mother earned a science degree there. Donaldson gained a BA degree in mathematics from Pembroke College, Cambridge, in 1979, and in 1980 began postgraduate work at Worcester College, Oxford, at first under Nigel Hitchin and later under Michael Atiyah's supervision. Still a postgraduate student, Donaldson proved in 1982 a result that would establish his fame. He published the result in a paper "Self-dual connections and the topology of sm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge
Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge became an important trading centre during the Roman and Viking ages, and there is archaeological evidence of settlement in the area as early as the Bronze Age. The first town charters were granted in the 12th century, although modern city status was not officially conferred until 1951. The city is most famous as the home of the University of Cambridge, which was founded in 1209 and consistently ranks among the best universities in the world. The buildings of the university include King's College Chapel, Cavendish Laboratory, and the Cambridge University Library, one of the largest legal deposit libraries in the world. The city's skyline is dominated by several college buildings, along with the spire of the Our Lady and the English Martyrs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gábor Székelyhidi
Gábor Székelyhidi (born 30 June 1981 in Debrecen) is a Hungarian mathematician, specializing in differential geometry. Gábor Székelyhidi, the brother of László Székelyhidi, graduated from Trinity College, Cambridge with a bachelor's degree in 2002 (part 3 of Tripos 2003 with honours) and received from Imperial College London his PhD in 2006 under the supervision of Simon Donaldson with thesis ''Extremal metrics and K-stability''. Székelyhidi was a postdoc at Harvard University and was from 2008 to 2011 Ritt Assistant Professor at Columbia University. At the University of Notre Dame he became an assistant professor in 2011, an associate professor in 2014, and in 2016 a full professor. His research deals with geometric analysis and complex differential geometry (Kähler manifolds), including the existence of canonical metrics (such as extremal Kähler and Kähler-Einstein metrics) on projective manifolds, and the relations between extremal metrics and K-stability for pola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crafoord Prize
The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foundation in Lund. The Academy is responsible for selecting the Crafoord Laureates. The prize is awarded in four categories: astronomy and mathematics; Geology, geosciences; Biology, biosciences, with particular emphasis on ecology; and polyarthritis, the disease from which Holger severely suffered in his last years. According to the Academy, "these disciplines are chosen so as to complement those for which the Nobel Prizes are awarded". Only one award is given each year, according to a rotating scheme – astronomy and mathematics; then geosciences; then biosciences. A Crafoord Prize in polyarthritis is only awarded when a special committee decides that substantial progress in the field has been made. The recipient of the Crafoord Prize is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Medal
The Royal Medal, also known as The Queen's Medal and The King's Medal (depending on the gender of the monarch at the time of the award), is a silver-gilt medal, of which three are awarded each year by the Royal Society, two for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences", done within the Commonwealth of Nations. Background The award was created by George IV of the United Kingdom, George IV and awarded first during 1826. Initially there were two medals awarded, both for the most important discovery within the year previous, a time period which was lengthened to five years and then shortened to three. The format was endorsed by William IV of the United Kingdom, William IV and Victoria of the United Kingdom, Victoria, who had the conditions changed during 1837 so that mathematics was a subject for which a Royal Medal could be awarded, albeit only every third year. The conditions were chang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG in 2013–14, the Fields Medal came closely after the Abel Prize as the second most prestigious international award in mathematics. The prize includes a monetary award which, since 2006, has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Junior Whitehead Prize
The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whitehead. More specifically, people being considered for the award must be resident in the United Kingdom on 1 January of the award year or must have been educated in the United Kingdom. Also, the candidates must have less than 15 years of work at the postdoctorate level and must not have received any other prizes from the Society. Since the inception of the prize, no more than two could be awarded per year, but in 1999 this was increased to four "to allow for the award of prizes across the whole of mathematics, including applied mathematics, mathematical physics, and mathematical aspects of computer science". The Senior Whitehead Prize has similar residence requirements and rules concerning prior prizes, but is intended to recognize more exper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-stability Of Fano Varieties
In mathematics, and in particular algebraic geometry, K-stability is an algebro-geometric stability condition for projective algebraic varieties and complex manifolds. K-stability is of particular importance for the case of Fano varieties, where it is the correct stability condition to allow the formation of moduli spaces, and where it precisely characterises the existence of Kähler–Einstein metrics. K-stability was first defined for Fano manifolds by Gang Tian in 1997 in response to a conjecture of Shing-Tung Yau from 1993 that there should exist a stability condition which characterises the existence of a Kähler–Einstein metric on a Fano manifold. It was defined in reference to the ''K-energy functional'' previously introduced by Toshiki Mabuchi. Tian's definition of K-stability was reformulated by Simon Donaldson in 2001 in a purely algebro-geometric way. K-stability has become an important notion in the study and classification of Fano varieties. In 2012 Xiuxiong Chen, D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-stability
In mathematics, and especially differential geometry, differential and algebraic geometry, K-stability is an Algebraic Geometry, algebro-geometric stability condition, for complex manifolds and complex algebraic variety, complex algebraic varieties. The notion of K-stability was first introduced by Tian Gang, Gang Tian and reformulated more algebraically later by Simon Donaldson. The definition was inspired by a comparison to geometric invariant theory (GIT) stability. In the K-stability of Fano varieties, special case of Fano variety, Fano varieties, K-stability precisely characterises the existence of Kähler–Einstein metrics. More generally, on any compact complex manifold, K-stability is #Yau–Tian–Donaldson Conjecture, conjectured to be equivalent to the existence of constant scalar curvature Kähler metrics (cscK metrics). History In 1954, Eugenio Calabi formulated a conjecture about the existence of Kähler metrics on compact Kähler manifolds, now known as the Calabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kobayashi–Hitchin Correspondence
In differential geometry, algebraic geometry, and gauge theory, the Kobayashi–Hitchin correspondence (or Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The correspondence is named after Shoshichi Kobayashi and Nigel Hitchin, who independently conjectured in the 1980s that the moduli spaces of stable vector bundles and Einstein–Hermitian vector bundles over a complex manifold were essentially the same.Shoshichi Kobayashi, Curvature and stability of vector bundles, Proc. Japan Acad. Ser. A. Math. Sci., 58 (1982), 158-162.Nigel Hitchin, Nonlinear problems in geometry, Proc. Sixth Int. Symp., Sendai/Japan (1979; Zbl 0433.53002) This was proven by Simon Donaldson for projective algebraic surfaces and later for projective algebraic manifolds,Donaldson, S.K., 1985. Anti self‐dual Yang‐Mills connections over complex algebraic surfaces and stable vector bundles. Proceedings of the London Mathematica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donaldson–Thomas Theory
In mathematics, specifically algebraic geometry, Donaldson–Thomas theory is the theory of Donaldson–Thomas invariants. Given a compact moduli space of sheaves on a Calabi–Yau threefold, its Donaldson–Thomas invariant is the virtual number of its points, i.e., the integral of the cohomology class 1 against the virtual fundamental class. The Donaldson–Thomas invariant is a holomorphic analogue of the Casson invariant. The invariants were introduced by . Donaldson–Thomas invariants have close connections to Gromov–Witten invariants of algebraic three-folds and the theory of stable pairs due to Rahul Pandharipande and Thomas. Donaldson–Thomas theory is physically motivated by certain BPS states that occur in string and gauge theorypg 5. This is due to the fact the invariants depend on a stability condition on the derived category D^b(\mathcal) of the moduli spaces being studied. Essentially, these stability conditions correspond to points in the Kahler moduli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donaldson Theorem
In mathematics, and especially differential topology and gauge theory, Donaldson's theorem states that a definite intersection form of a compact, oriented, smooth manifold of dimension 4 is diagonalisable. If the intersection form is positive (negative) definite, it can be diagonalized to the identity matrix (negative identity matrix) over the . The original version of the theorem required the manifold to be simply connected, but it was later improved to apply to 4-manifolds with any fundamental group. History The theorem was proved by Simon Donaldson. This was a contribution cited for his Fields medal in 1986. Idea of proof Donaldson's proof utilizes the moduli space \mathcal_P of solutions to the anti-self-duality equations on a principal \operatorname(2)-bundle P over the four-manifold X. By the Atiyah–Singer index theorem, the dimension of the moduli space is given by :\dim \mathcal = 8k - 3(1-b_1(X) + b_+(X)), where c_2(P)=k, b_1(X) is the first Betti number of X and b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donaldson Theory
In mathematics, and especially gauge theory, Donaldson theory is the study of the topology of smooth 4-manifolds using moduli spaces of anti-self-dual instantons. It was started by Simon Donaldson (1983) who proved Donaldson's theorem restricting the possible quadratic forms on the second cohomology group of a compact simply connected 4-manifold. Important consequences of this theorem include the existence of an Exotic R4 and the failure of the smooth h-cobordism theorem in 4 dimensions. The results of Donaldson theory depend therefore on the manifold having a differential structure, and are largely false for topological 4-manifolds. Many of the theorems in Donaldson theory can now be proved more easily using Seiberg–Witten theory, though there are a number of open problems remaining in Donaldson theory, such as the Witten conjecture and the Atiyah–Floer conjecture. See also * Kronheimer–Mrowka basic class * Instanton * Floer homology * Yang–Mills equations In physi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
