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Resurgence Asymptotics in String Theory

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No logo availableInstitut des Hautes Études Scientifiques (IHÉS)
 Schiappa, Ricardo

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Resurgence Asymptotics in String Theory
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4
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Following up on the morning lecture, I will give a very light introduction to resurgent asymptotics. These techniques will then be explored (again in the spirit of a light introduction) within transseries solutions of topological string theory, themselves obtained via a nonperturbative completion of the holomorphic anomaly equations.
Keywords
00:00
String theoryTheoryRadiusSeries (mathematics)AsymptoteComplex (psychology)Plane (geometry)Borel-MengeMathematical singularityCoefficientPerturbation theoryThermal expansionSinguläres IntegralInverse elementStokes' theoremHolomorphic functionFunction (mathematics)Formal power seriesPoint (geometry)Pole (complex analysis)Analytic continuationCurvatureExponential functionTerm (mathematics)Parameter (computer programming)Axiom of choiceNichtlineares GleichungssystemRandbedingung <Mathematik>DisintegrationHierarchyAutomorphismDerivation (linguistics)CalculusOperator (mathematics)Multiplication signDifferent (Kate Ryan album)Food energyAnalytic continuationPlane (geometry)Musical ensembleSeries (mathematics)Nichtlineares GleichungssystemInfinity2 (number)RadiusAsymptoteTransformation (genetics)Thermal expansionThetafunktionCoefficientOrder (biology)CalculationNumerical analysisUniverse (mathematics)Term (mathematics)Many-sorted logicFormal power seriesPower seriesMathematical singularityObject (grammar)Arithmetic meanOrdinary differential equationPole (complex analysis)Group actionBoundary value problemPotenz <Mathematik>Heat transferParameter (computer programming)Sigma-algebraStandard deviationFunction (mathematics)1 (number)INTEGRALRoundness (object)LogarithmPerturbation theoryQuantum mechanicsWell-formed formulaExpressionSocial classLoop (music)RecursionSummierbarkeitHierarchyAxiom of choiceStress (mechanics)Holomorphic functionResidual (numerical analysis)Point (geometry)ModulformSet theoryComplex numberDirection (geometry)Algebraic structureLine (geometry)Derivation (linguistics)Category of beingString theoryEnergy levelOperator (mathematics)PhysicalismComplex (psychology)Inverse elementFactory (trading post)ComputabilityDifferential topologyInstantonFirst-order logicQuantumPower (physics)Computer animation
09:42
Analytic continuationStokes' theoremOperator (mathematics)Standard deviationDerivation (linguistics)Latent heatDirected setSeries (mathematics)LogarithmString theoryRegular graphEquationInvariant (mathematics)CalculusCategory of beingOrder (biology)Ordinary differential equationThermal expansionParameter (computer programming)Axiom of choiceRandbedingung <Mathematik>DisintegrationNichtlineares GleichungssystemBorel-MengeTerm (mathematics)ChainPrice indexAutomorphismTranslation (relic)Vector spaceAsymptoteBuildingTopologyTheoryFood energyApproximationComplete metric spaceFactory (trading post)AverageBlock (periodic table)InstantonAlgebraic structureWeightMathematical singularityNumerical analysisRight angleGame theoryModulformObject (grammar)Derivation (linguistics)ExpressionPower (physics)Connectivity (graph theory)Standard deviationSummierbarkeitEstimatorMany-sorted logicPerturbation theoryAxiom of choiceIterationSeries (mathematics)Category of beingArithmetic meanMultiplication signDivisorAutomorphismRule of inferenceConvolutionEquationProduct (business)Term (mathematics)Slide ruleChainCommutatorFirst-order logicStokes' theoremOrdinary differential equationTheoryResidual (numerical analysis)Rational numberFormal power seriesWell-formed formulaPhysicalismPerpetual motionVector fieldPartition function (statistical mechanics)Analytic continuationPower seriesSigma-algebraTranslation (relic)Invariant (mathematics)Plane (geometry)Potenz <Mathematik>Regular graphThetafunktionDirection (geometry)Mass flow rateDifferent (Kate Ryan album)Order (biology)Network topologyBuildingTransformation (genetics)Latent heatString theoryPositional notationThermal expansionCombinatoricsDescriptive statisticsGeometryBoundary value problemAsymptoteLogical constantLine (geometry)Rational functionMetrePoint (geometry)Moment (mathematics)Parameter (computer programming)Transverse waveOperator (mathematics)Stokes-PhänomenComputer animation
19:23
TopologyThermal expansionBuildingSeries (mathematics)AsymptoteComplete metric spaceApproximationBorel-MengePlane (geometry)Stokes' theoremLine (geometry)InfinityInstantonRelation <Mathematik>Function (mathematics)INTEGRALTheoremMathematical analysisAsymptotic analysisMultiplicationAutomorphismParameter (computer programming)Term (mathematics)Content (media)Logical constantOscillationSummierbarkeitFaktorenanalyseCoefficientExtension (kinesiology)Group actionInflection pointAdditionMatrix (mathematics)Model theoryGauge theoryTheoryEquationSupergravityString theoryLocal ringGravitationTerm (mathematics)Power (physics)Derivation (linguistics)Thermal expansionLoop (music)InstantonDivisorInfinityConnected spaceAsymptoteFunction (mathematics)Well-formed formulaPerturbation theoryTheoremModulformClosed setExpressionString theoryComputabilityNetwork topologyCombinatoricsOrder (biology)Dot productLattice (group)SummierbarkeitMultiplicationGroup actionPerpetual motionPartition function (statistical mechanics)Logical constantPotenz <Mathematik>IntegerMany-sorted logicSymmetry (physics)Arrow of timeDirection (geometry)Series (mathematics)Statistical hypothesis testingElementary arithmeticLocal ringAnalytic continuationTheory of relativityThetafunktionSigma-algebraResonatorPlane (geometry)Rational numberApproximationMathematical singularityChainInfinite setNumerical analysisGoodness of fitFilm editingDifferent (Kate Ryan album)RootLine (geometry)Multiplication signEnergy levelNormal (geometry)TheoryAlgebraic structureModel theorySequenceDescriptive statisticsMusical ensembleFactory (trading post)DispersionsrelationClassical physicsCartesian coordinate systemRight angleDiagramSocial classObject (grammar)Group representationGenerating set of a groupPartition (number theory)Stokes' theoremConnectivity (graph theory)Computer animation
28:44
String theoryTheoryFood energyModel theoryTopologyLocal ringGeometrySurfaceSpacetimeComplex (psychology)Algebraic structureHolomorphic functionBoundary value problemEquationNichtlineares GleichungssystemYukawa potentialAutocovarianceDerivation (linguistics)Independence (probability theory)Function (mathematics)Partition (number theory)Insertion lossStandard deviationSpacetimeBoundary value problemSurfaceOperator (mathematics)Different (Kate Ryan album)Order (biology)AsymptoteGroup action1 (number)String theoryThermal expansionEquationRecursionDerivation (linguistics)Local ring2 (number)ComputabilityGenerating set of a groupExpressionCurvePropagatorComplex (psychology)Algebraic structureNetwork topologyMatrix (mathematics)Nichtlineares GleichungssystemHolomorphic functionRiemann surfaceOrdinary differential equationInstantonFrequencyDuality (mathematics)Arrow of timeFiber bundlePerturbation theoryCoordinate systemPartition function (statistical mechanics)Differential equationINTEGRALPartition (number theory)Regular graphCalculationFlow separationVector potentialWell-formed formulaModule (mathematics)Perpetual motionAnalogySummierbarkeitAutocovarianceFormal power seriesArithmetic meanSlide ruleWave packetNormal (geometry)Series (mathematics)Presentation of a groupModel theoryMorphismusObject (grammar)Dot productMeasurementLine (geometry)Point (geometry)Parameter (computer programming)Musical ensembleMultiplication signGeometryComputer animation
37:58
Complex (psychology)Algebraic structureSpacetimeHausdorff dimensionEquationStandard deviationInsertion lossHolomorphic functionNichtlineares GleichungssystemGroup actionFrequencyGeometryRecursionConnected spaceTopologyLimit (category theory)String theoryFunction (mathematics)Partition (number theory)Local ringFood energySurfaceBoundary value problemPoint (geometry)1 (number)Cubic graphRootThermal expansionRelation <Mathematik>Term (mathematics)Stokes' theoremAsymptoteSeries (mathematics)TheoryHomomorphismusDerivation (linguistics)Limit (category theory)Group actionSummierbarkeitSeries (mathematics)RecursionPotenz <Mathematik>Generating set of a groupPolynomialHolomorphic functionConnectivity (graph theory)SequenceString theoryNetwork topologyNichtlineares GleichungssystemFlow separationEquationDifferential operatorMany-sorted logicInstantonPairwise comparisonDifferent (Kate Ryan album)RootLimit of a functionLocal ringTerm (mathematics)Combinatory logicModel theoryStandard deviationCubic graphPoint (geometry)DiffusionsgleichungPartition function (statistical mechanics)Parameter (computer programming)Set theoryWell-formed formulaOperator (mathematics)GeometryComputabilityPredictabilityFrequencySpacetimeDimensional analysisEinheitswurzelComplex (psychology)Algebraic structureEuklidischer RaumPerturbation theoryFunction (mathematics)Statistical hypothesis testingStochastic kernel estimationGrothendieck topologySlide ruleCausalityComputer animation
47:11
1 (number)Cubic graphRootString theoryPlane (geometry)Group actionPoint (geometry)Parameter (computer programming)Keilförmige AnordnungComplex (psychology)Asymptotic analysisTheorySpacetimeRadiusModulo (jargon)Local ringBorel-MengePropagatorHolomorphic functionMereologySequenceImaginary numberGreatest elementStatistical hypothesis testingProcess capability indexInflection pointUniformer RaumHill differential equationAsymptoteSeries (mathematics)Thermal expansionFood energyComplete metric spaceApproximationChainFree groupModel theoryMatrix (mathematics)Geometric quantizationPositional notationStokes' theoremGroup actionPerturbation theoryApproximationPoint (geometry)Dot productRadiusPolygonGraph coloringResultantFilm editingNumerical analysisConsistencyNumerical digitStokes-PhänomenComplex numberOrder (biology)SequenceTerm (mathematics)Function (mathematics)Different (Kate Ryan album)Complex (psychology)InstantonWave packetWeightCycle (graph theory)Pairwise comparisonMathematical singularityPower (physics)Arrow of timeSheaf (mathematics)Figurate numberAnalytic continuationRight angleSeries (mathematics)Statistical hypothesis testingObject (grammar)String theoryEnergy levelPiMassLine (geometry)TheoryLocal ringSlide ruleSpacetimePrice indexComplete metric spaceNetwork topologyPropagatorGreen's functionLogical constantCurve2 (number)Near-ringBoundary value problemOperator (mathematics)AsymptoteMultiplication signHolomorphic functionNichtlineares GleichungssystemCoordinate systemLatent heatTransformation (genetics)Algebraic structureModel theoryScalar fieldModule (mathematics)Goodness of fitRational functionComputer animation
56:25
Stokes' theoremHydraulic jumpDifferent (Kate Ryan album)Complete metric spaceString theoryFunction (mathematics)Partition (number theory)SpacetimeGeometric quantizationModel theoryMatrix (mathematics)Thermal expansionDeterminantDirection (geometry)Quantum field theoryGauge theoryLogical constantBorel-MengeAlgebraic structureSurfacePhysicsAsymptotic analysisTheoryPerturbation theoryMultiplicationWave packetDuality (mathematics)Factory (trading post)Degree (graph theory)Film editingSeries (mathematics)Different (Kate Ryan album)Axiom of choiceGroup actionRight angleString theoryPartition function (statistical mechanics)Invariant (mathematics)Model theoryDifferential equationPotenz <Mathematik>Parameter (computer programming)CoefficientPerturbation theoryTerm (mathematics)Boundary value problemStokes-PhänomenResultantExpected valueDeterminantMany-sorted logicThermal expansionGeometric quantizationLocal ringOcean currentMatrix (mathematics)SpacetimeFunction (mathematics)Inverse elementMultiplication signMatching (graph theory)PhysicalismHydraulic jumpNichtlineares GleichungssystemEnergy levelPower (physics)Symmetry (physics)Social classMathematical singularityCurveTheoryLengthDescriptive statisticsGenerating set of a groupPoint (geometry)MeasurementPartition (number theory)Forcing (mathematics)DiagramInstantonFraction (mathematics)Cartesian coordinate systemComputabilityObject (grammar)Order (biology)Loop (music)SequenceClique-widthStatistical hypothesis testingRecurrence relationLogical constantSquare numberGroup representationRootTransformation (genetics)Network topologyDerivation (linguistics)Lecture/Conference
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