0000000000347945

AUTHOR

Jörg Frauendiener

showing 5 related works from this author

Computational approach to compact Riemann surfaces

2017

International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…

[ MATH ] Mathematics [math]Fundamental groupEquations[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]Holomorphic functionGeneral Physics and AstronomyFOS: Physical sciences010103 numerical & computational mathematics01 natural sciencessymbols.namesakeMathematics - Algebraic Geometrynumerical methodsFOS: MathematicsSpectral Methods0101 mathematics[MATH]Mathematics [math]Algebraic Geometry (math.AG)Mathematical PhysicsMathematicsCurvesKadomtsev-Petviashvili equationCollocationNonlinear Sciences - Exactly Solvable and Integrable SystemsPlane (geometry)Applied MathematicsRiemann surface010102 general mathematicsMathematical analysisStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Methods of contour integrationHyperelliptic Theta-FunctionsRiemann surfacessymbolsDispersion Limit[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]Algebraic curveExactly Solvable and Integrable Systems (nlin.SI)Complex plane
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Efficient computation of the branching structure of an algebraic curve

2012

An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant points of the curve are constructed via a minimal spanning tree of the discriminant points. This leads to paths of minimal length between the points, which is important for a later stage where these paths are used as integration contours to compute periods of the surface. The branching structure of the surface is obtained by analytically continuing the roots of the equation defining the algebraic curve along the constructed generators of the fundamental gro…

Discrete mathematicsCircular algebraic curveComputational Geometry (cs.CG)FOS: Computer and information sciencesStable curveApplied MathematicsButterfly curve (algebraic)010102 general mathematics010103 numerical & computational mathematics01 natural sciencesModular curveMathematics - Algebraic GeometryComputational Theory and Mathematics14Q05Algebraic surfaceFOS: MathematicsComputer Science - Computational GeometryAlgebraic functionAlgebraic curve0101 mathematicsHyperelliptic curveAlgebraic Geometry (math.AG)AnalysisMathematics
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New horizons for fundamental physics with LISA

2022

K. G. Arun et al.

AstrofísicaPROTOPLANET MIGRATIONFísica-Modelos matemáticosPhysics and Astronomy (miscellaneous)gr-qcFOS: Physical sciencesGeneral Relativity and Quantum Cosmology (gr-qc)GRAVITATIONAL-WAVEShorizonFundamental physicGeneral Relativity and Quantum CosmologyPhysics Particles & FieldsGravitational wavesLIGO (Observatory)Tests of general relativitySettore FIS/05 - Astronomia e AstrofisicaDARK-MATTERFísica matemáticaKOZAI MECHANISMHigh Energy PhysicsGENERAL-RELATIVITYFundamental physics; Gravitational waves; LISA; Tests of general relativityFundamental physicsPRIMORDIAL BLACK-HOLESLISAScience & TechnologyGeneral Relativity and Cosmology83CXXPhysicsgravitation: interactiongravitational radiationFísicaCompactQUANTUM-GRAVITYPhysical SciencesAstronomia[PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc]fundamental physics; gravitational waves; LISA; test of general relativityMODIFIED GRAVITYtest of general relativityGravitational waveMULTIPOLE MOMENTSHUBBLE CONSTANT
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Blow-up of the non-equivariant 2+1 dimensional wave map

2014

It has been known for a long time that the equivariant 2+1 wave map into the 2-sphere blows up if the initial data are chosen appropriately. Here, we present numerical evidence for the stability of the blow-up phenomenon under explicit violations of equivariance.

Mathematics::K-Theory and HomologyMathematical analysisOne-dimensional spaceMathematics::Analysis of PDEsEquivariant mapGeneral MedicineStability (probability)Mathematics::Algebraic TopologyMathematical PhysicsMathematics35L67 35L70 65M20 65P10 74H35
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Algebraic Curves and Riemann Surfaces in Matlab

2010

In the previous chapter, a detailed description of the algorithms for the ‘algcurves’ package in Maple was presented. As discussed there, the package is able to handle general algebraic curves with coefficients given as exact arithmetic expressions, a restriction due to the use of exact integer arithmetic. Coefficients in terms of floating point numbers, i.e., the representation of decimal numbers of finite length on a computer, can in principle be handled, but the floating point numbers have to be converted to rational numbers. This can lead to technical difficulties in practice. One also faces limitations if one wants to study families of Riemann surfaces, where the coefficients in the al…

Moduli of algebraic curvesAlgebraRiemann–Hurwitz formulaRiemann hypothesissymbols.namesakeGeometric function theoryRiemann surfaceComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONAlgebraic surfacesymbolsRiemann's differential equationBranch pointMathematics
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