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Shinichi Mochizuki
is a Japanese mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry. His contributions include his solution of the Grothendieck conjecture in anabelian geometry about hyperbolic curves over number fields. Mochizuki has also worked in Hodge–Arakelov theory and p-adic Teichmüller theory. Mochizuki developed inter-universal Teichmüller theory, which has attracted attention from non-mathematicians due to claims it provides a resolution of the ''abc'' conjecture. Biography Early life Shinichi Mochizuki was born to parents Kiichi and Anne Mochizuki. When he was five years old, Shinichi Mochizuki and his family left Japan to live in the United States. His father was Fellow of the Center for International Affairs and Center for Middle Eastern Studies at Harvard University (1974–76). Mochizuki attended Phillips Exeter Academy and graduated in 1985. Mochizuki entered Princeton University as an undergraduate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tokyo
Tokyo (; ja, 東京, , ), officially the Tokyo Metropolis ( ja, 東京都, label=none, ), is the capital and largest city of Japan. Formerly known as Edo, its metropolitan area () is the most populous in the world, with an estimated 37.468 million residents ; the city proper has a population of 13.99 million people. Located at the head of Tokyo Bay, the prefecture forms part of the Kantō region on the central coast of Honshu, Japan's largest island. Tokyo serves as Japan's economic center and is the seat of both the Japanese government and the Emperor of Japan. Originally a fishing village named Edo, the city became politically prominent in 1603, when it became the seat of the Tokugawa shogunate. By the mid-18th century, Edo was one of the most populous cities in the world with a population of over one million people. Following the Meiji Restoration of 1868, the imperial capital in Kyoto was moved to Edo, which was renamed "Tokyo" (). Tokyo was devastate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phillips Exeter Academy
(not for oneself) la, Finis Origine Pendet (The End Depends Upon the Beginning) gr, Χάριτι Θεοῦ (By the Grace of God) , location = 20 Main Street , city = Exeter, New Hampshire , zipcode = 03833 , type = Independent school, Independent, Day school, day & boarding school, boarding , established = , founder = John Phillips (educator), John PhillipsElizabeth Phillips , ceeb = 300185 , grades = Ninth grade#United States, 9–Twelfth grade#United States, 12 , head = William K. Rawson , faculty = 217 , gender = Coeducational , enrollment = 1,096 total865 boarding214 day , class = 12 students , ratio = 5:1 , athletics = 22 Interscholastic sports62 Interscholastic teams , conference = NEPS ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quanta Magazine
''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science. ''Undark Magazine'' described ''Quanta Magazine'' as "highly regarded for its masterful coverage of complex topics in science and math." The science news aggregator ''RealClearScience'' ranked ''Quanta Magazine'' first on its list of "The Top 10 Websites for Science in 2018." In 2020, the magazine received a National Magazine Award for General Excellence from the American Society of Magazine Editors for its "willingness to tackle some of the toughest and most difficult topics in science and math in a language that is accessible to the lay reader without condescension or oversimplification." The articles in the magazine are freely available to read online. ''Scientific American'', ''Wired'', ''The Atlantic'', and ''The Washington Post'', as well as international science publications like ''Spektrum der Wissensch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Stix
Jakob M. Stix (born in 1974) is a German mathematician. He specializes in arithmetic algebraic geometry (étale fundamental group, anabelian geometry and other topics). Stix studied mathematics in Freiburg and Bonn and received his doctorate in 2002 from Florian Pop at the University of Bonn (''Projective Anabelian Curves in Positive Characteristic and Descent Theory for Log-Etale Covers''). His dissertation was awarded the best doctoral thesis of the year 2002 by the Mathematical Institute of the University of Bonn. He was a post-doctoral student at the Institute for Advanced Study. In 2008, he became junior research group leader at the Mathematics Center of the University of Heidelberg, where he habilitated Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ... in 2011 (''Evidence for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Scholze
Peter Scholze (; born 11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018. He has been called one of the leading mathematicians in the world. He won the Fields Medal in 2018, which is regarded as the highest professional honor in mathematics. Early life and education Scholze was born in Dresden and grew up in Berlin. His father is a physicist, his mother a computer scientist, and his sister studied chemistry. He attended the in Berlin-Friedrichshain, a gymnasium devoted to mathematics and science. As a student, Scholze participated in the International Mathematical Olympiad, winning three gold medals and one silver medal. He studied at the University of Bonn and completed his bachelor's degree in three semesters and his master's degree in two further semesters. He obtained his Ph.D. in 2012 under the supervisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vojta Conjecture
In mathematics, Vojta's conjecture is a conjecture introduced by about heights of points on algebraic varieties over number fields. The conjecture was motivated by an analogy between diophantine approximation and Nevanlinna theory (value distribution theory) in complex analysis. It implies many other conjectures in Diophantine approximation, Diophantine equations, arithmetic geometry, and mathematical logic. Statement of the conjecture Let F be a number field, let X/F be a non-singular algebraic variety, let D be an effective divisor on X with at worst normal crossings, let H be an ample divisor on X, and let K_X be a canonical divisor on X. Choose Weil height functions h_H and h_ and, for each absolute value v on F, a local height function \lambda_. Fix a finite set of absolute values S of F, and let \epsilon>0. Then there is a constant C and a non-empty Zariski open set U\subseteq X, depending on all of the above choices, such that :: \sum_ \lambda_(P) + h_(P) \le \epsilon h_H(P) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Szpiro Conjecture
In number theory, Szpiro's conjecture relates to the conductor and the discriminant of an elliptic curve. In a slightly modified form, it is equivalent to the well-known ''abc'' conjecture. It is named for Lucien Szpiro, who formulated it in the 1980s. Szpiro's conjecture and its equivalent forms have been described as "the most important unsolved problem in Diophantine analysis" by Dorian Goldfeld, in part to its large number of consequences in number theory including Roth's theorem, the Mordell conjecture, the Fermat–Catalan conjecture, and Brocard's problem. Original statement The conjecture states that: given ε > 0, there exists a constant ''C''(ε) such that for any elliptic curve ''E'' defined over Q with minimal discriminant Δ and conductor ''f'', we have : \vert\Delta\vert \leq C(\varepsilon ) \cdot f^. Modified Szpiro conjecture The modified Szpiro conjecture states that: given ε > 0, there exists a constant ''C''(ε) su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Geometry
In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations. Four theorems in Diophantine geometry which are of fundamental importance include: * Mordell–Weil Theorem * Roth's Theorem * Siegel's Theorem * Faltings's Theorem Background Serge Lang published a book ''Diophantine Geometry'' in the area in 1962, and by this book he coined the term "Diophantine Geometry". The traditional arrangement of material on Diophantine equations was by degree and number of variables, as in Mordell's ''Diophantine Equations'' (1969). Mordell's book starts with a remark on homogeneous equations ''f'' = 0 over the rational field, attributed to C. F. Gauss, that non-zero solutions in integers (even primitive lattice points) exist if non-zero rational solutions do, and notes a caveat of L. E. D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tate Curve
In mathematics, the Tate curve is a curve defined over the ring of formal power series \mathbb q with integer coefficients. Over the open subscheme where ''q'' is invertible, the Tate curve is an elliptic curve. The Tate curve can also be defined for ''q'' as an element of a complete field of norm less than 1, in which case the formal power series converge. The Tate curve was introduced by in a 1959 manuscript originally titled "Rational Points on Elliptic Curves Over Complete Fields"; he did not publish his results until many years later, and his work first appeared in . Definition The Tate curve is the projective plane curve over the ring Z of formal power series with integer coefficients given (in an affine open subset of the projective plane) by the equation : y^2+xy=x^3+a_4x+a_6 where :-a_4=5\sum_n \frac = 5q+45q^2+140q^3+\cdots :-a_6=\sum_\frac\times\frac = q+23q^2+154q^3+\cdots are power series with integer coefficients. The Tate curve over a complete field Suppose that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frobenioid
In arithmetic geometry, a Frobenioid is a category with some extra structure that generalizes the theory of line bundles on models of finite extensions of global fields. Frobenioids were introduced by . The word "Frobenioid" is a portmanteau of Frobenius and monoid, as certain Frobenius morphisms between Frobenioids are analogues of the usual Frobenius morphism, and some of the simplest examples of Frobenioids are essentially monoids. The Frobenioid of a monoid If ''M'' is a commutative monoid, it is acted on naturally by the monoid ''N'' of positive integers under multiplication, with an element ''n'' of ''N'' multiplying an element of ''M'' by ''n''. The Frobenioid of ''M'' is the semidirect product of ''M'' and ''N''. The underlying category of this Frobenioid is category of the monoid, with one object and a morphism for each element of the monoid. The standard Frobenioid is the special case of this construction when ''M'' is the additive monoid of non-negative integers. Elemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of International Congresses Of Mathematicians Plenary And Invited Speakers
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." The current list of Plenary and Invited Speakers presented here is based on the ICM's post-WW II terminology, in which the one-hour speakers in the morning sessions are called "Plenary Speakers" and the other speakers (in the afternoon sessions) whose talks are included in the ICM published proceedings are called "Invited Speakers". In the pre-WW II congresses the Plenary Speakers were called "Invited Speakers". By congress year 1897, Zürich * Jules Andrade * Léon Autonne *Émile Borel * N. V. Bougaïev *Francesco Brioschi *Hermann Brunn *Cesare Burali-Forti *Charles Jean de la Vallée Poussin *Gustaf Eneström *Federigo Enriques *Gino Fano * Zoel García de Galdeano * Francesco Gerbaldi *Paul Gordan *Jacques Hadamard * Adolf Hurwitz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nilcurve
In mathematics, a nilcurve is a pointed stable curve over a finite field with an indigenous bundle whose ''p''-curvature is square nilpotent. Nilcurves were introduced by as a central concept in his theory of p-adic Teichmüller theory In mathematics, ''p''-adic Teichmüller theory describes the "uniformization" of ''p''-adic curves and their moduli, generalizing the usual Teichmüller theory that describes the uniformization of Riemann surfaces and their moduli. It was intr .... The nilcurves form a stack over the moduli stack of stable genus ''g'' curves with ''r'' marked points in characteristic ''p'', of degree ''p''3''g''–3+''r''. References * *{{Citation , last1=Mochizuki , first1=Shinichi , title=A theory of ordinary p-adic curves , doi=10.2977/prims/1195145686 , mr=1437328 , year=1996 , journal=Kyoto University. Research Institute for Mathematical Sciences. Publications , issn=0034-5318 , volume=32 , issue=6 , pages=957–1152, doi-access=free Algeb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
