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Random construction of Riemann surfaces
"... Partially supported by the NSF Grant DMS0072534In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? By a Riemann surface, we mean an oriented surface with a complete, finitearea metric of constant curvature1. In the ..."
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Cited by 23 (4 self)
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Partially supported by the NSF Grant DMS0072534In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? By a Riemann surface, we mean an oriented surface with a complete, finitearea metric of constant curvature1
the Riemann
"... We consider the problem of characterizing topologically the action of a Kleinian group on ..."
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We consider the problem of characterizing topologically the action of a Kleinian group on
PoissonDirichlet distribution for random Belyi surfaces
 Ann. Probab
, 2006
"... Abstract. Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a “typical” compact Riemann surface of large genus based on compactifying finitearea Riemann surfaces associated ..."
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Cited by 8 (0 self)
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Abstract. Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a “typical” compact Riemann surface of large genus based on compactifying finitearea Riemann surfaces
Riemann
, 1998
"... A gas of N Bogomol’nyi vortices in the Abelian Higgs model is studied on a compact Riemann surface of genus g and area A. The volume of the moduli space is computed and found to depend on N, g and A, but not on other details of the shape of the surface. The volume is then used to find the thermodyna ..."
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A gas of N Bogomol’nyi vortices in the Abelian Higgs model is studied on a compact Riemann surface of genus g and area A. The volume of the moduli space is computed and found to depend on N, g and A, but not on other details of the shape of the surface. The volume is then used to find
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: n n
Holography and Riemann surfaces
 Adv. Theor. Math. Phys
, 2000
"... We study holography for asymptotically AdS spaces with an arbitrary genus compact Riemann surface as the conformal boundary. Such spaces can be constructed from the Euclidean AdS3 by discrete identifications; the discrete groups one uses are the socalled classical Schottky groups. As we show, the s ..."
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Cited by 21 (4 self)
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We study holography for asymptotically AdS spaces with an arbitrary genus compact Riemann surface as the conformal boundary. Such spaces can be constructed from the Euclidean AdS3 by discrete identifications; the discrete groups one uses are the socalled classical Schottky groups. As we show
The symplectic nature of fundamental groups of surfaces
 ADV. MATH
, 1984
"... A symplectic structure on a manifold is a closed nondegenerate exterior 2form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metric which is Klhler. Many moduli spaces associated with Riemann surfaces have such Kahler structures: the ..."
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Cited by 221 (8 self)
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A symplectic structure on a manifold is a closed nondegenerate exterior 2form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metric which is Klhler. Many moduli spaces associated with Riemann surfaces have such Kahler structures
RIEMANN”.
, 904
"... One shows that Cartan’s method of adapted frames in Chapter XII of his famous treatise of Riemannian geometry, leads to a classification theorem of homogeneous Riemannian manifolds. Examples of classification in 3D dimensions obtained by Cartan are given using this powerful method. AMS 1991 subject ..."
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One shows that Cartan’s method of adapted frames in Chapter XII of his famous treatise of Riemannian geometry, leads to a classification theorem of homogeneous Riemannian manifolds. Examples of classification in 3D dimensions obtained by Cartan are given using this powerful method. AMS 1991 subject classifications. Primary 53C30
Results 1  10
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