|
Ian Agol
Ian Agol (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds. Education and career Agol graduated with B.S. in mathematics from the California Institute of Technology in 1992 and obtained his Ph.D. in 1998 from the University of California, San Diego. At UCSD, his advisor was Michael Freedman and his thesis was ''Topology of Hyperbolic 3-Manifolds''. He is a professor at the University of California, Berkeley and a former professor at the University of Illinois at Chicago. Contributions In 2004, Agol proved the Marden tameness conjecture, a conjecture of Albert Marden. It states that a hyperbolic 3-manifold with finitely generated fundamental group is homeomorphic to the interior of a compact 3-manifold. The conjecture was also independently proven by Danny Calegari and David Gabai, and implies the Ahlfors measure conjecture. In 2012 he announced a proof of the virtually Haken conjecture, which was published ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aarhus University
Aarhus University ( da, Aarhus Universitet, abbreviated AU) is a public research university with its main campus located in Aarhus, Denmark. It is the second largest and second oldest university in Denmark. The university is part of the Coimbra Group, the Guild, and Utrecht Network of European universities and is a member of the European University Association. The university was founded in Aarhus, Denmark, in 1928 and comprises five faculties in Arts, Natural Sciences, Technical Sciences, Health, and Business and Social Sciences and has a total of twenty-seven departments. It is home to over thirty internationally recognised research centres, including fifteen centres of excellence funded by the Danish National Research Foundation. The university has been ranked among the top 100 world's best universities. ''Times Higher Education'' ranks Aarhus University in the top 10 of the most beautiful universities in Europe (2018). The university's alumni include Bjarne Stroustrup, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clay Research Award
__NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class="wikitable sortable" , - ! Year !! Winner !! Citation , - , 2022 , , Søren Galatius and Oscar Randal-Williams John Pardon , , "for their profound contributions to the understanding of high dimensional manifolds and their diffeomorphism groups; they have transformed and reinvigorated the subject." "in recognition of his wide-ranging and transformative work in geometry and topology, particularly his groundbreaking achievements in symplectic topology." , - , 2021 , , Bhargav Bhatt , , "For his groundbreaking achievements in commutative algebra, arithmetic algebraic geometry, and topology in the p-adic setting." , - , 2020 , , not awarded , - , 2019 , , Wei Zhang Tristan Buckmaster, Philip Isett and Vlad Vicol , , "In recog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ahlfors Measure Conjecture
In mathematics, the Ahlfors conjecture, now a theorem, states that the limit set of a finitely-generated Kleinian group is either the whole Riemann sphere, or has measure 0. The conjecture was introduced by , who proved it in the case that the Kleinian group has a fundamental domain Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each o ... with a finite number of sides. proved the Ahlfors conjecture for topologically tame groups, by showing that a topologically tame Kleinian group is geometrically tame, so the Ahlfors conjecture follows from Marden's tameness conjecture that hyperbolic 3-manifolds with finitely generated fundamental groups are topologically tame (homeomorphic to the interior of compact 3-manifolds). This latter conjecture was proved, independently, by and by . als ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Gabai
David Gabai is an American mathematician and the Hughes-Rogers Professor of Mathematics at Princeton University. Focused on low-dimensional topology and hyperbolic geometry, he is a leading researcher in those subjects. Biography David Gabai received his B.S. in mathematics from MIT in 1976 and his Ph.D. in mathematics from Princeton University in 1980. Gabai completed his doctoral dissertation, titled "Foliations and genera of links", under the supervision of William Thurston. After positions at Harvard and University of Pennsylvania, Gabai spent most of the period of 1986–2001 at Caltech, and has been at Princeton since 2001. Gabai was the Chair of the Department of Mathematics at Princeton University from 2012 to 2019. Honours and awards In 2004, David Gabai was awarded the Oswald Veblen Prize in Geometry, given every three years by the American Mathematical Society. He was an invited speaker in the International Congress of Mathematicians 2010, Hyderabad on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Danny Calegari
Danny Matthew Cornelius Calegari is a mathematician who is currently a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory. Education and career In 1994, Calegari received a B.A. in Mathematics from the University of Melbourne with honors. He received his Ph.D. in 2000 from the University of California, Berkeley under the joint supervision of Andrew Casson and William Thurston; his dissertation concerned foliations of three-dimensional manifolds. From 2000–2002 he was Benjamin Peirce Assistant Professor at Harvard University, after which he joined the California Institute of Technology faculty; he became Merkin Professor in 2007. He was a University Professor of Pure Mathematics at the University of Cambridge in 2011–2012, and has been a Professor of Mathematics at the University of Chicago since 2012. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", i.e. that the space not exclude any ''limiting values'' of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other top ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homeomorphic
In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word ''homeomorphism'' comes from the Greek words '' ὅμοιος'' (''homoios'') = similar or same and '' μορφή'' (''morphē'') = shape or form, introduced to mathematics by Henri Poincaré in 1895. Very roughly speaking, a topological space is a geometric object, and the homeomorphism is a continuous stretching and bending of the object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a torus are not. However, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamental Group
In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of the topological space. The fundamental group is the first and simplest homotopy group. The fundamental group is a homotopy invariant—topological spaces that are homotopy equivalent (or the stronger case of homeomorphic) have isomorphic fundamental groups. The fundamental group of a topological space X is denoted by \pi_1(X). Intuition Start with a space (for example, a surface), and some point in it, and all the loops both starting and ending at this point— paths that start at this point, wander around and eventually return to the starting point. Two loops can be combined in an obvious way: travel along the first loop, then along the second. Two loops are considered equivalent if one can be deformed into the other without breaki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address is now in Denver, Colorado. CMI's scientific activities are managed from the President's office in Oxford, United Kingdom. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the sponsorship of Boston businessman Landon T. Clay. Harvard mathematician Arthur Jaffe was the first president of CMI. While the institute is best known for its Millennium Prize Problems, it carries out a wide range of activities, including a postdoctoral program (ten Clay Research Fellows are supported currently), conferences, workshops, and summer schools. Governance The institute is run according to a standard structure comprising a scientific advisory committee that decides on grant-awarding and research proposals, and a board of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Marden
Albert Marden (born 18 November 1934) is an American mathematician, specializing in complex analysis and hyperbolic geometry. Education and career Marden received his PhD in 1962 from Harvard University with thesis advisor Lars Ahlfors. Marden has been a professor at the University of Minnesota since the 1970s, where he is now professor emeritus. He was a member of the Institute for Advanced Study (IAS) in the academic year 1969–70, Fall 1978, and Fall 1987. His research deals with Riemann surfaces, quadratic differentials, Teichmüller spaces, hyperbolic geometry of surfaces and 3-manifolds, Fuchsian groups, Kleinian groups, complex dynamics, and low-dimensional geometric analysis. Concerning properties of hyperbolic 3-manifolds, Marden formulated in 1974 the tameness conjecture, which was proved in 2004 by Ian Agol and independently by a collaborative effort of Danny Calegari and David Gabai. In 1962, he gave a talk (as an approved speaker but not an invited speaker) on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Illinois At Chicago
The University of Illinois Chicago (UIC) is a public research university in Chicago, Illinois. Its campus is in the Near West Side community area, adjacent to the Chicago Loop. The second campus established under the University of Illinois system, UIC is also the largest university in the Chicago metropolitan area, having more than 33,000 students enrolled in 16 colleges. It is classified among "R1: Doctoral Universities – Very high research activity." The roots of UIC can be traced to the establishment of the Chicago College of Pharmacy in 1859, which was joined in the 1800s by additional medical related schools. It began an undergraduate program toward the end of World War II, and developed its West side campus in the 1960s. In 1982, it consolidated the University of Illinois at Chicago Circle and the University of Illinois at the Medical Center into the present university. Today, the university has become a global leader for a number of subjects, such as nursing, pharmac ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_(14592057920).jpg "Click for more on -> University Of Illinois At Chicago")