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Hyam Rubinstein
Joachim Hyam Rubinstein FAA (born 7 March 1948, in Melbourne) an Australian top mathematician specialising in low-dimensional topology; he is currently serving as an honorary professor in the Department of Mathematics and Statistics at the University of Melbourne, having retired in 2019. He has spoken and written widely on the state of the mathematical sciences in Australia, with particular focus on the impacts of reduced Government spending for university mathematics departments. Education In 1965, Rubinstein matriculated (i.e. graduated) from Melbourne High School in Melbourne, Australia winning the maximum of four exhibitions. In 1969, he graduated from Monash University in Melbourne, with a B.Sc.(Honours) degree in mathematics. In 1974, Rubinstein received his Ph.D. from the University of California, Berkeley under the advisership of John Stallings. His dissertation was on the topic of ''Isotopies of Incompressible Surfaces in Three Dimensional Manifolds''. Resea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Research Institute Of Oberwolfach
The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazis in order to further the German war effort, which at that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melbourne
Melbourne ( ; Boonwurrung/Woiwurrung: ''Narrm'' or ''Naarm'') is the capital and most populous city of the Australian state of Victoria, and the second-most populous city in both Australia and Oceania. Its name generally refers to a metropolitan area known as Greater Melbourne, comprising an urban agglomeration of 31 local municipalities, although the name is also used specifically for the local municipality of City of Melbourne based around its central business area. The metropolis occupies much of the northern and eastern coastlines of Port Phillip Bay and spreads into the Mornington Peninsula, part of West Gippsland, as well as the hinterlands towards the Yarra Valley, the Dandenong and Macedon Ranges. It has a population over 5 million (19% of the population of Australia, as per 2021 census), mostly residing to the east side of the city centre, and its inhabitants are commonly referred to as "Melburnians". The area of Melbourne has been home to Aboriginal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regina (program)
Regina is a suite of mathematical software for 3-manifold topologists. It focuses upon the study of 3-manifold triangulations and includes support for normal surfaces and angle structures. Features * Regina implements a variant of Rubinstein's 3-sphere recognition algorithm. This is an algorithm that determines whether or not a triangulated 3-manifold is homeomorphic to the 3-sphere. * Regina further implements the connect-sum decomposition. This will decompose a triangulated 3-manifold into a connect-sum of triangulated prime 3-manifolds. * Homology and Poincare duality for 3-manifolds, including the torsion linking form. * Includes portions of the SnapPea kernel for some geometric calculations. * Has both a GUI and Python interface. See also * Computational topology Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Scharlemann
Martin George Scharlemann (born 6 December 1948) is an American topologist who is a professor at the University of California, Santa Barbara. He obtained his Ph.D. from the University of California, Berkeley under the guidance of Robion Kirby in 1974. A conference in his honor was held in 2009 at the University of California, Davis. He is a Fellow of the American Mathematical Society, for his "contributions to low-dimensional topology and knot theory." Abigail Thompson was a student of his. Together they solved the graph planarity problem: There is an algorithm to decide whether a finite graph in 3-space can be moved in 3-space into a plane. He gave the first proof of the classical theorem that knots with unknotting number one are prime. He used hard combinatorial arguments for this. Simpler proofs are now known. Selected publications *"Producing reducible 3-manifolds by surgery on a knot" ''Topology'' 29 (1990), no. 4, 481–500. *with Abigail Thompson, "Heegaard splittings ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below. Introduction Definition A topological space ''X'' is a 3-manifold if it is a second-countable Hausdorff space and if every point in ''X'' has a neighbourhood that is homeomorphic to Euclidean 3-space. Mathematical theory of 3-manifolds The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds. Phenomena in three dimensions can be strikingly different from phenomena in other dimensions, and so there is a prevalence of very specialized techniques that do not generalize to dimensions g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle measurements at known points, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration. In computer vision Computer stereo vision and optical 3D measuring systems use this principle to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base ''b'' and must be known. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Jaco
William "Bus" H. Jaco (born July 14, 1940 in Grafton, West Virginia) is an American mathematician who is known for his role in the Jaco–Shalen–Johannson decomposition theorem and is currently Regents Professor and Grayce B. Kerr Chair at Oklahoma State University and Executive Director of the Initiative for Mathematics Learning by Inquiry. Education and career Jaco received a B.A from the Fairmont State College and an M.A. from Pennsylvania State University. He completed his Ph.D. in 1968 at the University of Wisconsin-Madison. He held faculty positions at the University of Michigan and Rice University before joining the faculty at Oklahoma State University as Head of the Mathematics Dept. from 1982–87 and again served as head from 2011–2018. He has been a member of the Institute for Advanced Study, (IAS) the Mathematical Sciences Research Institute (MSRI), and the American Institute of Mathematics (AIM). He served as the Executive Director of the American Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Surface
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum. Definitions Minimal surfaces can be defined in several equivalent ways in R3. The fact that they are equivalent serves to demonstrate how minimal surface theory lies at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegaard Splitting
In the mathematical field of geometric topology, a Heegaard splitting () is a decomposition of a compact oriented 3-manifold that results from dividing it into two handlebodies. Definitions Let ''V'' and ''W'' be handlebodies of genus ''g'', and let ƒ be an orientation reversing homeomorphism from the boundary of ''V'' to the boundary of ''W''. By gluing ''V'' to ''W'' along ƒ we obtain the compact oriented 3-manifold : M = V \cup_f W. Every closed, orientable three-manifold may be so obtained; this follows from deep results on the triangulability of three-manifolds due to Moise. This contrasts strongly with higher-dimensional manifolds which need not admit smooth or piecewise linear structures. Assuming smoothness the existence of a Heegaard splitting also follows from the work of Smale about handle decompositions from Morse theory. The decomposition of ''M'' into two handlebodies is called a Heegaard splitting, and their common boundary ''H'' is called the Heegaard surf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Stallings
John Robert Stallings Jr. (July 22, 1935 – November 24, 2008) was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley 6, Stallings proved that ordinary Euclidean ''n''-dimensional space has a unique piecewise linear, hence also smooth, structure, if ''n'' is not equal to 4. This took on added significance when, as a consequence of work of Michael Freedman and Simon Donaldson in 1982, it was shown that 4-space has exotic smooth structures, in fact uncountably many such. In a 1963 paper Stallings constructed an example of a finitely presented group with infinitely generated 3-dimensional integral homology group and, moreover, not of the type F_3 , that is, not admitting a classifying space with a finite 3-skeleton. This example came to be called the ''Stallings group'' and is a key example in the study of homological fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Honours Degree
Honours degree has various meanings in the context of different degrees and education systems. Most commonly it refers to a variant of the undergraduate bachelor's degree containing a larger volume of material or a higher standard of study, or both, rather than an "ordinary", "general" or "pass" bachelor's degree. Honours degrees are sometimes indicated by "Hons" after the degree abbreviation, with various punctuation according to local custom, e.g. "BA (Hons)", "B.A., Hons", etc. In Canada, honours degrees may be indicated with an "H" preceding the degree abbreviation, e.g. "HBA" for Honours Bachelor of Arts or Honours Business Administration. Examples of honours degree include the ''honors bachelor's degree'' in the United States; the ''bachelor's degree with honours'' in the United Kingdom, Bangladesh, Hong Kong, and India; the ''honours bachelor's degree'' in Ireland; the ''bachelor with honours'' and ''bachelor honours degree'' in New Zealand; the ''bachelor with honours'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
