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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 selfduality equations on a Riemann surface
 Proc. Lond. Math. Soc., III. Ser
, 1987
"... In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled 'instanton ..."
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Cited by 501 (6 self)
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In this paper we shall study a special class of solutions of the selfdual YangMills equations. The original selfduality equations which arose in mathematical physics were defined on Euclidean 4space. The physically relevant solutions were the ones with finite action—the socalled &apos
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
A Mean Value Theorem for Closed Geodesics on Congruence Surfaces
, 2008
"... Abstract. We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an important role in the study of statistics of the eigen ..."
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Cited by 1 (0 self)
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Abstract. We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an important role in the study of statistics
The Mean Square of Weighted Multiplicity Function
, 2008
"... Abstract. We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an important role in the study of statistics of the eigen ..."
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Abstract. We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an important role in the study of statistics
Modeling the Interaction of Light Between Diffuse Surfaces
, 1984
"... A method is described which models the interaction of light between diffusely reflecting surfaces. Current light reflection models used in computer graphics do not account for the objecttoobject reflection between diffuse surfaces, and thus incorrectly compute the global illumination effects. The ..."
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Cited by 393 (6 self)
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. The new procedure, based on methods used in thermal engineering, includes the effects of diffuse light sources of finite area, as well as the "colorbleeding" effects which are caused by the diffuse reflections. A simple environment is used to illustrate these simulated effects and is presented
Liouville Correlation Functions from Fourdimensional Gauge Theories
 SIMONS CENTER FOR GEOMETRY AND PHYSICS, STONY BROOK UNIVERSITY
, 2009
"... We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N = 2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture ..."
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Cited by 391 (22 self)
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We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N = 2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture
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
Riemann surfaces
 Princeton Mathematical Series
, 1960
"... Propósito: Recientemente se ha hipotetizado que la proteína nuclear p63 es el primer marcador de las células madres del epitelio corneal durante el desarrollo. La presente publicación determina la localización de las células queratolimbales madres del epitelio corneal por el patrón de expresión p63 ..."
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Cited by 111 (0 self)
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Propósito: Recientemente se ha hipotetizado que la proteína nuclear p63 es el primer marcador de las células madres del epitelio corneal durante el desarrollo. La presente publicación determina la localización de las células queratolimbales madres del epitelio corneal por el patrón de expresión p63 en la superficie ocular. Métodos: Se usó tejido queratolimbal humano para detectar por inmunohistoquimia el patrón de expresión de la proteína p63. Se desarrolló la hibridización in situ bidireccional para confirmar la expresión p63 mRNA en el anillo queratolimbal. Resultados: La proteína p63 y ARNm se expresaron sólo en los núcleos de la capa basal de las células epiteliales limbales. Conclusión: De acuerdo con nuestros hallazgos, la proteína p63 localizada en la células basales del epitelio queratolimbal es un buen marcador para detectar las células madres del epitelio corneal. La p63 podría utilizarse en práctica clínica para determinar la actividad de las células madres del epitelio corneal. Palabras clave: P63, limbo corneal, células madre, epitelio corneal. SUMMARY
ElectricMagnetic duality and the geometric Langlands program
, 2006
"... The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t H ..."
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Cited by 292 (26 self)
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The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t
Results 1  10
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318,501