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6/6 Automorphic Forms and Optimization in Euclidean Space

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6/6 Automorphic Forms and Optimization in Euclidean Space
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6
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6
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The goal of this lecture course, “Automorphic Forms and Optimization in Euclidean Space”, is to prove the universal optimality of the E8 and Leech lattices. This theorem is the main result of a recent preprint “Universal Optimality of the E8 and Leech Lattices and Interpolation Formulas”, written in collaboration with H. Cohn, A. Kumar, S/D/ Miller and D. Radchenko.
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FundamentalbereichPlane (geometry)Well-formed formulaNeighbourhood (graph theory)Line (geometry)Group actionCategory of beingElement (mathematics)Matrix normInterpolationMatrix (mathematics)Power (physics)Gamma functionResultantNormal (geometry)Point (geometry)Multiplication signFunctional (mathematics)GeometryWaveFunktionalgleichungComplex numberModulformVector spaceTime domainAlgebraic closurePropagatorPropositional formulaCoordinate systemFrobenius methodSummierbarkeitLecture/Conference
Normed vector spacePoint (geometry)EstimatorGroup actionDivisorTime domainPlane (geometry)Frobenius methodSubsetElement (mathematics)Complex numberOperator (mathematics)Absolute valueMatrix normGamma functionDirection (geometry)Logical constantPosition operatorFunctional (mathematics)Algebraic closureMorphismusEquivalence relationTerm (mathematics)Multiplication signRight angleMatrix (mathematics)Price indexEinheitswurzelDeterminantNormal (geometry)FundamentalbereichDimensional analysisQuotientInverse elementStability theoryFundamental theorem of algebraLecture/Conference
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IcosahedronPole (complex analysis)Open setDimensional analysisFunctional (mathematics)Negative numberInfinityCondition numberCausalitySign (mathematics)Presentation of a groupOptimization problemMultiplication signSquare numberNormal (geometry)Variable (mathematics)GeometrySimilarity (geometry)Fourier seriesMathematicsSet theoryDressing (medical)Numerical analysisRadiusGroup representationPlane (geometry)Point (geometry)Coordinate systemAnalytic number theoryArithmetic meanFourier transformProduct (business)Linear programmingTerm (mathematics)Right anglePropositional formulaUncertainty principleInequality (mathematics)Line (geometry)Invariant (mathematics)Boundary value problemInterpolationDifferent (Kate Ryan album)SpacetimeTime domainIntegerLine integralBound statePotenz <Mathematik>Price indexClassical physicsMereologyPole (complex analysis)Stochastic kernel estimationCategory of beingTransformation (genetics)Lecture/Conference
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GradientExponential functionRational numberDimensional analysisAlgebraic numberInterpolationDifferent (Kate Ryan album)Functional (mathematics)Image resolutionGoodness of fitConfiguration spaceResultantContinuous functionOptimization problemRootPoint (geometry)Term (mathematics)LogarithmNumerical analysisDerivation (linguistics)Regular graphPhysicalismFourier transformParameter (computer programming)Fourier seriesIntegerCategory of beingUniqueness quantificationTransformation (genetics)Closed setMathematical optimizationUniverse (mathematics)Differential equationSummierbarkeitDirac delta functionCoefficientNatural numberDistribution (mathematics)Basis <Mathematik>LinearizationCombinatory logicOpen setMultiplication signPole (complex analysis)Lecture/Conference
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Matrix (mathematics)Series (mathematics)Functional (mathematics)Ring (mathematics)Goodness of fitModulformPoint (geometry)Lattice (group)Dimensional analysisFourier seriesRootReal numberDegree (graph theory)2 (number)Configuration spaceSequenceMathematical optimizationNatural numberInterpolationSineFinite differenceDifferential equationEvoluteMereologyThermal expansionOpen setFourier transformOptimization problemResultantSign (mathematics)Numerical analysisRadiusMathematicsEuklidischer RaumLecture/Conference
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Hadamard matrix
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