Formal & Physical Sciences MathematicsENRepresentations of GL2Richard E BorcherdsJuly 16, 2024 34 min★ ★ ★ ★ ★ 5/5Representation TheoryGL2Langlands Program
Formal & Physical Sciences MathematicsENMordell-Weil theoremRichard E BorcherdsMay 5, 2024 21 min★ ★ ★ ★ ★ 5/5Mordell-Weil TheoremElliptic CurvesAbelian Varieties
Formal & Physical Sciences MathematicsENSelberg trace formulaRichard E BorcherdsApril 16, 2024 27 min★ ★ ★ ★ ★ 5/5Selberg Trace FormulaSL2(R)Representation Theory
Formal & Physical Sciences MathematicsENRiemann mapping theoremRichard E BorcherdsMarch 19, 2024 26 min★ ★ ★ ★ ★ 5/5Complex AnalysisRiemann Mapping TheoremConformal Mapping
Formal & Physical Sciences MathematicsENVinberg lecture part 4. Automorphic formsRichard E BorcherdsMarch 10, 2024 36 min★ ★ ★ ★ ★ 5/5Automorphic FormsHyperbolic Reflection GroupsKac-Moody Algebras
Formal & Physical Sciences MathematicsENVinberg lecture part 3. Kac-Moody algebrasRichard E BorcherdsMarch 6, 2024 50 min★ ★ ★ ★ ★ 5/5Kac-Moody AlgebrasVinberg GroupsRoot Multiplicities
Formal & Physical Sciences MathematicsENVinberg lecture part 2. The reflection group of II25,1Richard E BorcherdsMarch 1, 2024 62 min★ ★ ★ ★ ★ 5/5Vinberg AlgorithmReflection GroupsLorentzian Lattices
Formal & Physical Sciences MathematicsENVinberg lecture part 1.Vinberg's algorithmRichard E BorcherdsFebruary 29, 2024 61 min★ ★ ★ ★ ★ 5/5Vinberg's AlgorithmReflection GroupsLorentzian Lattices
Formal & Physical Sciences MathematicsENElliptic functions lecture 4. The sigma functionRichard E BorcherdsFebruary 24, 2024 24 min★ ★ ★ ★ ★ 5/5Elliptic FunctionsSigma FunctionTheta Functions
Formal & Physical Sciences MathematicsENBorwein integralsRichard E BorcherdsFebruary 22, 2024 13 min★ ★ ★ ★ ★ 5/5Borwein IntegralsSinc FunctionFourier Transform
Formal & Physical Sciences MathematicsENElliptic functions lecture 3. Jacobi functionsRichard E BorcherdsFebruary 21, 2024 32 min★ ★ ★ ★ ☆ 4/5Elliptic FunctionsJacobi FunctionsLine Bundles
Formal & Physical Sciences MathematicsENElliptic functions lecture 2Richard E BorcherdsFebruary 19, 2024 35 min★ ★ ★ ★ ★ 5/5Elliptic FunctionsWeierstrass P FunctionAddition Formula
Formal & Physical Sciences MathematicsENElliptic functions 1. Weierstrass function.Richard E BorcherdsFebruary 18, 2024 32 min★ ★ ★ ★ ★ 5/5Elliptic FunctionsWeierstrass FunctionComplex Analysis
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 53. Three calculators for number theoristsRichard E BorcherdsApril 24, 2022 12 min★ ★ ★ ★ ☆ 4/5Number TheoryCalculatorsPrime Factorization
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 52. Nonvanishing of L series at s=1.Richard E BorcherdsApril 22, 2022 24 min★ ★ ★ ★ ★ 5/5Number TheoryDirichlet L-SeriesAnalytic Number Theory
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 51. Proof of Dirichlet's theoremRichard E BorcherdsApril 20, 2022 24 min★ ★ ★ ★ ★ 5/5Number TheoryDirichlet's TheoremL-Series
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 50. Dirichlet charactersRichard E BorcherdsApril 18, 2022 20 min★ ★ ★ ★ ★ 5/5Number TheoryDirichlet CharactersL-Functions
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 49. Dirichlet's theoremRichard E BorcherdsApril 16, 2022 35 min★ ★ ★ ★ ★ 5/5Number TheoryDirichlet's TheoremDirichlet Characters
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 48 Proof of the prime number theoremRichard E BorcherdsApril 14, 2022 17 min★ ★ ★ ★ ★ 5/5Prime Number TheoremNumber TheoryRiemann Zeta Function
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 47. The prime number theoremRichard E BorcherdsApril 12, 2022 27 min★ ★ ★ ★ ★ 5/5Prime Number TheoremAnalytic Number TheoryRiemann Zeta Function
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 46. Products of Dirichlet seriesRichard E BorcherdsApril 10, 2022 17 min★ ★ ★ ★ ★ 5/5Dirichlet SeriesNumber TheoryMöbius Inversion
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 45 Dirichlet seriesRichard E BorcherdsApril 8, 2022 31 min★ ★ ★ ★ ★ 5/5Number TheoryDirichlet SeriesRiemann Zeta Function
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 44 Pythagorean trianglesRichard E BorcherdsApril 6, 2022 23 min★ ★ ★ ★ ★ 5/5Number TheoryPythagorean TriplesBinary Quadratic Forms
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 43 Gaussian integersRichard E BorcherdsApril 4, 2022 35 min★ ★ ★ ★ ★ 5/5Gaussian IntegersNumber TheorySums of Two Squares
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 42. Examples of indefinite binary quadratic forms.Richard E BorcherdsApril 2, 2022 22 min★ ★ ★ ★ ★ 5/5Number TheoryBinary Quadratic FormsIndefinite Forms
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 41: More examples of binary quadratic formsRichard E BorcherdsMarch 31, 2022 29 min★ ★ ★ ★ ★ 5/5Number TheoryBinary Quadratic FormsClass Numbers
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 40. Examples of positive definite formsRichard E BorcherdsMarch 29, 2022 28 min★ ★ ★ ★ ★ 5/5Number TheoryQuadratic FormsPositive Definite
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 39: Equivalence of binary quadratic formsRichard E BorcherdsMarch 27, 2022 22 min★ ★ ★ ★ ★ 5/5Number TheoryBinary Quadratic FormsEquivalence
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 38. Binary quadratic formsRichard E BorcherdsMarch 25, 2022 23 min★ ★ ★ ★ ★ 5/5Number TheoryBinary Quadratic FormsDiscriminant
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 37 Continued fractionsRichard E BorcherdsMarch 23, 2022 26 min★ ★ ★ ★ ★ 5/5Number TheoryContinued FractionsPell's Equation
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 36 Kronecker symbolRichard E BorcherdsMarch 21, 2022 21 min★ ★ ★ ★ ★ 5/5Kronecker SymbolNumber TheoryQuadratic Reciprocity
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 35 Jacobi symbolRichard E BorcherdsMarch 19, 2022 38 min★ ★ ★ ★ ★ 5/5Jacobi SymbolNumber TheoryQuadratic Reciprocity
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 34. Gauss sumsRichard E BorcherdsMarch 17, 2022 17 min★ ★ ★ ★ ★ 5/5Number TheoryGauss SumsQuadratic Reciprocity
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 33. Quadratic reciprocityRichard E BorcherdsMarch 15, 2022 32 min★ ★ ★ ★ ★ 5/5Number TheoryQuadratic ReciprocityLegendre Symbol
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 32. Calculation of the Legendre symbolRichard E BorcherdsMarch 13, 2022 28 min★ ★ ★ ★ ★ 5/5Number TheoryLegendre SymbolQuadratic Residues
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 31. Quadratic residues.Richard E BorcherdsMarch 11, 2022 32 min★ ★ ★ ★ ★ 5/5Number TheoryQuadratic ResiduesLegendre Symbol
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 30. Fields in number theoryRichard E BorcherdsMarch 9, 2022 24 min★ ★ ★ ★ ★ 5/5Number TheoryFieldsFinite Fields
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 29. Rings in number theoryRichard E BorcherdsMarch 7, 2022 38 min★ ★ ★ ★ ★ 5/5Number TheoryRingsIdeals
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 28. Products of groupsRichard E BorcherdsMarch 5, 2022 23 min★ ★ ★ ★ ★ 5/5Group TheoryNumber TheoryChinese Remainder Theorem
Formal & Physical Sciences MathematicsENIntroduction to number theory lecture 27. Groups and number theoryRichard E BorcherdsMarch 3, 2022 29 min★ ★ ★ ★ ★ 5/5Group TheoryNumber TheoryFermat's Theorem