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June Huh
June Huh (full name: June E Huh, ; born 1983) is an Korean-American mathematician who is currently a professor at Princeton University. Previously, he was a professor at Stanford University. He was awarded the Fields Medal in 2022 and a MacArthur Fellowship in 2022. He has been noted for the linkages that he has found between algebraic geometry and combinatorics. Early life and education Huh was born in Stanford, California while his parents were completing graduate school at Stanford University. He was raised in South Korea, where his family returned when he was approximately two years old. His father was a professor of statistics at Korea University, while his mother was a professor of Russian language at Seoul National University. Poor scores on elementary school tests convinced him that he was not very good at math. He dropped out of high school to focus on writing poetry after becoming bored and exhausted by the routine of studying. Because of this, he has been des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Korea University
Korea University (KU, ) is a private research university in Seoul, South Korea, established in 1905. The university is included as one of the SKY universities, a popular acronym referring to Korea's three most prestigious universities. The student body consists of over 20,000 undergraduate students and over 10,000 graduate students. The university has 81 departments in 19 colleges and divisions, as well as 18 graduate schools. It has over 1,500 full-time faculty members with over 95% of them holding Ph.D. or equivalent qualification in their field. The Korea University Alumni Association consists of more than 280,000 university graduates. Korea University is a large research institution, notable in South Korean history for being the first educational institution to offer academic programs in Korea in various disciplines, such as law, economics and journalism. It is particularly well known for its College of Law. Korea University also has auxiliary educational facilities suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristic Polynomial Of Matroids
In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the language of partially ordered sets, a finite matroid is equivalent to a geometric lattice. Matroid theory borrows extensively from the terminology of both linear algebra and graph theory, largely because it is the abstraction of various notions of central importance in these fields. Matroids have found applications in geometry, topology, combinatorial optimization, network theory and coding theory. Definition There are many equivalent ( cryptomorphic) ways to define a (finite) matroid.A standard source for basic definitions and results about matroids is Oxley (1992). An older standard source is Welsh (1976). See Brylawski' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eric Katz
Eric Katz is a mathematician working in combinatorial algebraic geometry and arithmetic geometry. He is currently an associate professor in the Department of Mathematics at Ohio State University. In joint work with Karim Adiprasito and June Huh, he resolved the Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Joseph Rabinoff and David Zureick-Brown, he has given bounds on rational and torsion points on curves. Education Katz went to Beachwood High School, in Beachwood, Ohio, a suburb of Cleveland. After earning a B.S. in Mathematics from Ohio State University in 1999, he pursued graduate studies at Stanford University, obtaining his Ph.D. in 2004 with a thesis written under the direction of Yakov Eliashberg and Ravi Vakil Ravi D. Vakil (born February 22, 1970) is a Canadian-American mathematician working in algebraic geometry. Education and career Vakil attended high school at Martingrove Collegiate Institute i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karim Adiprasito
Karim Alexander Adiprasito (born 1988) is a German mathematician working at the University of Copenhagen and the Hebrew University of Jerusalem who works in combinatorics. He completed his Ph.D. in 2013 at Free University Berlin under the supervision of Günter M. Ziegler. He has been a professor at the Hebrew University since 2015, and at the University of Copenhagen since 2019. He is of German and Indonesian descent, and bears an Indonesian surname. He was awarded the 2015 European Prize in Combinatorics for his work in discrete geometry, in particular on realization spaces of polytopes citing "his wide-ranging and deep contributions to discrete geometry using analytic methods particularly for his solution of old problems of Perles and Shephard (going back to Legendre and Steinitz) on projectively unique polyhedra." In joint work with June Huh and Eric Katz, he resolved the Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chromatic Polynomial
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to study the four color problem. It was generalised to the Tutte polynomial by Hassler Whitney and W. T. Tutte, linking it to the Potts model of statistical physics. History George David Birkhoff introduced the chromatic polynomial in 1912, defining it only for planar graphs, in an attempt to prove the four color theorem. If P(G, k) denotes the number of proper colorings of ''G'' with ''k'' colors then one could establish the four color theorem by showing P(G, 4)>0 for all planar graphs ''G''. In this way he hoped to apply the powerful tools of analysis and algebra for studying the roots of polynomials to the combinatorial coloring problem. Hassler Whitney generalised Birkhoff’s polynomial from the planar case to general graphs in 1932. In 1968 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Read's Conjecture
Read's conjecture is a conjecture, first made by Ronald Read, about the unimodality of the coefficients of chromatic polynomials in the context of graph theory. In 1974, S. G. Hoggar tightened this to the conjecture that the coefficients must be strongly log-concave. Hoggar's version of the conjecture is called the Read–Hoggar conjecture. The Read–Hoggar conjecture had been unresolved for more than 40 years before June Huh proved it in 2009, during his PhD studies, using methods from algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...., pp. 2–4. References Conjectures that have been proved Graph theory {{graph-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sumner Byron Myers
Sumner Byron Myers (February 19, 1910 – October 8, 1955) was an American mathematician specializing in topology and differential geometry. He studied at Harvard University under H. C. Marston Morse, Tucker, A: Interview with Albert Tucker'', Princeton University, July 11, 1984. Last accessed January 1, 2010. where he graduated with a Ph.D. in 1932.Mathematics Genealogy Project: Sumner Byron Myers', no date. Last accessed December 5, 2005. Myers then pursued postdoctoral studies at Princeton University (1934–1936)Princeton University: Members of the School of Mathematics'', no date. Last accessed December 5, 2005. before becoming a professor for mathematics at the University of Michigan. He died unexpectedly from a heart attack during the 1955 Michigan–Army football game at Michigan Stadium. Sumner B. Myers Prize The Sumner B. Myers Prize was created in his honor for distinguished theses within the LSA Mathematics Department.University of Michigan: Sumner Myers Award', no d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Illinois Urbana-Champaign
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University of Illinois system and was founded in 1867. Enrolling over 56,000 undergraduate and graduate students, the University of Illinois is one of the largest public universities by enrollment in the country. The University of Illinois Urbana-Champaign is a member of the Association of American Universities and is classified among "R1: Doctoral Universities – Very high research activity". In fiscal year 2019, research expenditures at Illinois totaled $652 million. The campus library system possesses the second-largest university library in the United States by holdings after Harvard University. The university also hosts the National Center for Supercomputing Applications and is home to the fastest supercomputer on a university campus. The u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singularity Theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string. Perhaps the string will also touch itself without crossing, like an underlined "U". This is another kind of singularity. Unlike the double point, it is not ''stable'', in the sense that a small push will lift the bottom of the "U" away from the "underline". Vladimir Arnold defines the main goal of singularity theory as describing how objects depend on parameters, particularly in cases where the properties undergo sudden change under a small variation of the parameters. These ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heisuke Hironaka
is a Japanese mathematician who was awarded the Fields Medal in 1970 for his contributions to algebraic geometry. Career Hironaka entered Kyoto University in 1949. After completing his undergraduate studies at Kyoto University, he received his Ph.D. in 1960 from Harvard University while under the direction of Oscar Zariski. Hironaka held teaching positions at Brandeis University from 1960-1963, Columbia University in 1964, and Kyoto University from 1975 to 1988. He was a professor of mathematics at Harvard University from 1968 until becoming ''emeritus'' in 1992 and was a president of Yamaguchi University from 1996 to 2002. Research In 1964, Hironaka proved that singularities of algebraic varieties admit resolutions in characteristic zero. This means that any algebraic variety can be replaced by (more precisely is birationally equivalent to) a similar variety which has no singularities. He also introduced Hironaka's example showing that a deformation of Kähler manifolds need ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
