Related Research Articles
In mathematics, the uniformization theorem states that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the plane to arbitrary simply connected Riemann surfaces.
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object.
In mathematics, a topological group G is called a discrete group if there is no limit point in it. Equivalently, the group G is discrete if and only if its identity is isolated.
In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting on any of these spaces. There are some variations of the definition: sometimes the Fuchsian group is assumed to be finitely generated, sometimes it is allowed to be a subgroup of PGL(2,R), and sometimes it is allowed to be a Kleinian group which is conjugate to a subgroup of PSL(2,R).
Pierre Alphonse Laurent was a French mathematician, engineer, and Military Officer best known for discovering the Laurent series, an expansion of a function into an infinite power series, generalizing the Taylor series expansion.
Emanuel (Mannie) Ruben Piore was a scientist and a manager of industrial research.
In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable with PSL(2, C), is the quotient group of the 2 by 2 complex matrices of determinant 1 by their center, which consists of the identity matrix and its product by −1. PSL(2, C) has a natural representation as orientation-preserving conformal transformations of the Riemann sphere, and as orientation-preserving conformal transformations of the open unit ball B3 in R3. The group of Möbius transformations is also related as the non-orientation-preserving isometry group of H3, PGL(2, C). So, a Kleinian group can be regarded as a discrete subgroup acting on one of these spaces.
In mathematics, a Fuchsian model is a representation of a hyperbolic Riemann surface R as a quotient of the upper half-plane H by a Fuchsian group. Every hyperbolic Riemann surface admits such a representation. The concept is named after Lazarus Fuchs.
In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important because many examples of groups that arise throughout mathematics are locally compact and such groups have a natural measure called the Haar measure. This allows one to define integrals of Borel measurable functions on G so that standard analysis notions such as the Fourier transform and spaces can be generalized.
In mathematics, the Teichmüller space of a (real) topological surface is a space that parametrizes complex structures on up to the action of homeomorphisms that are isotopic to the identity homeomorphism. Teichmüller spaces are named after Oswald Teichmüller.
Nancy Ann Lynch is a computer scientist affiliated with the Massachusetts Institute of Technology. She is the NEC Professor of Software Science and Engineering in the EECS department and heads the "Theory of Distributed Systems" research group at MIT's Computer Science and Artificial Intelligence Laboratory.
Graduate Texts in Mathematics (GTM) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size. The GTM series is easily identified by a white band at the top of the book.
Lipman Bers was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism.
In mathematics, the special linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one:
Linda Jo Goldway Keen is an American mathematician and a fellow of the American Mathematical Society. Since 1965, she has been a professor in the Department of Mathematics and Computer Science at Lehman College of the City University of New York and a Professor of Mathematics at Graduate Center of the City University of New York.
John Robert Stallings Jr. 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 where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups.
Karen Vogtmann (born July 13, 1949 in Pittsburg, California) is an American mathematician working primarily in the area of geometric group theory. She is known for having introduced, in a 1986 paper with Marc Culler, an object now known as the Culler–Vogtmann Outer space. The Outer space is a free group analog of the Teichmüller space of a Riemann surface and is particularly useful in the study of the group of outer automorphisms of the free group on n generators, Out(Fn). Vogtmann is a professor of mathematics at Cornell University and the University of Warwick.
Lesley Millman Sibner was an American mathematician and professor of mathematics at Polytechnic Institute of New York University. She earned her Bachelors at City College CUNY in Mathematics. She completed her doctorate at Courant Institute NYU in 1964 under the joint supervision of Lipman Bers and Cathleen Morawetz. Her thesis concerned partial differential equations of mixed-type.
Irwin Kra is an American mathematician, who works on the function theory in complex analysis.
Rubí Elena Rodríguez Moreno is a Chilean mathematician in the department of mathematics and statistics at the University of La Frontera, a founder of the Iberoamerican Congress on Geometry, and the former president of the Chilean Mathematical Society. Her research specialties include complex geometry, Fuchsian groups, Riemann surfaces, and abelian varieties.
References
- ↑ Birth year from ISNI authority control file, retrieved 2018-11-27.
- 1 2 3 Curriculum vitae, February 8, 2013, retrieved 2014-06-14.
- ↑ Saxon, Wolfgang (May 12, 2000), "Emanuel Piore, 91, Leader And Researcher at I.B.M.", New York Times .
- ↑ Jane Piore Gilman at the Mathematics Genealogy Project
- ↑ Review of Two-generator Discrete Subgroups of PSL(2, R) by C. Maclachlan (1997), MR 1290281.
- ↑ Review of Complex Analysis: In the Spirit of Lipman Bers (2nd ed.) by Leonid V. Kovalev, MR 2986247
- ↑ 2014 Class of the Fellows of the AMS, retrieved 2014-06-16.
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
