Formal & Physical Sciences MathematicsENHomological algebra 6: Injective modulesRichard E BorcherdsOctober 31, 2020 29 min★ ★ ★ ★ ★ 5/5Injective ModulesHomological AlgebraEssential Extensions
Formal & Physical Sciences MathematicsENMath talk: Sporadic groups and number theoryRichard E BorcherdsOctober 30, 2020 27 min★ ★ ★ ★ ★ 5/5Sporadic GroupsMoonshineNumber Theory
Formal & Physical Sciences MathematicsENWeil conjectures 7: What is an etale morphism?Richard E BorcherdsOctober 29, 2020 29 min★ ★ ★ ★ ★ 5/5Etale MorphismAlgebraic GeometryWeil Conjectures
Formal & Physical Sciences MathematicsENHomological algebra 5: Ext(A,B)Richard E BorcherdsOctober 28, 2020 27 min★ ★ ★ ★ ★ 5/5Ext GroupsHomological AlgebraDerived Functors
Formal & Physical Sciences MathematicsENWeil conjectures 6: etale cohomology of a curveRichard E BorcherdsOctober 27, 2020 27 min★ ★ ★ ★ ☆ 4/5Etale CohomologyWeil ConjecturesAlgebraic Geometry
Formal & Physical Sciences MathematicsENHomological algebra 4: Properties of Tor over ringsRichard E BorcherdsOctober 26, 2020 29 min★ ★ ★ ★ ★ 5/5Homological AlgebraTor FunctorCommutative Algebra
Formal & Physical Sciences MathematicsENHomological algebra 3: Tor over ringsRichard E BorcherdsOctober 25, 2020 24 min★ ★ ★ ★ ☆ 4/5Homological AlgebraTor FunctorGroup Homology
Formal & Physical Sciences MathematicsENHomological algebra 2: properties of TorRichard E BorcherdsOctober 24, 2020 27 min★ ★ ★ ★ ★ 5/5Homological AlgebraTor FunctorAbelian Groups
Formal & Physical Sciences MathematicsENHomological algebra 1: Tor for abelian groupsRichard E BorcherdsOctober 23, 2020 22 min★ ★ ★ ★ ★ 5/5Homological AlgebraTor FunctorAbelian Groups
Formal & Physical Sciences MathematicsENWeil conjectures 5: Lefschetz trace formulaRichard E BorcherdsOctober 22, 2020 25 min★ ★ ★ ★ ☆ 4/5Weil ConjecturesLefschetz Trace FormulaÉtale Cohomology
Formal & Physical Sciences MathematicsENWeil conjectures 4 Fermat hypersurfacesRichard E BorcherdsOctober 20, 2020 21 min★ ★ ★ ★ ★ 5/5Weil ConjecturesFermat HypersurfacesGauss Sums
Formal & Physical Sciences MathematicsENCommutative algebra 44 Flat modulesRichard E BorcherdsOctober 19, 2020 16 min★ ★ ★ ★ ☆ 4/5Commutative AlgebraFlat ModulesProjective Modules
Formal & Physical Sciences MathematicsENCommutative algebra 43 (Stalkwise locally free modules)Richard E BorcherdsOctober 18, 2020 11 min★ ★ ★ ★ ★ 5/5Commutative AlgebraStalkwise Locally FreeProjective Modules
Formal & Physical Sciences MathematicsENCommutative algebra 42 Projective modulesRichard E BorcherdsOctober 17, 2020 22 min★ ★ ★ ★ ☆ 4/5Commutative AlgebraProjective ModulesLocally Free Modules
Formal & Physical Sciences MathematicsENCommutative algebra 41 Locally free modulesRichard E BorcherdsOctober 16, 2020 18 min★ ★ ★ ★ ★ 5/5Commutative AlgebraLocally Free ModulesVector Bundles
Formal & Physical Sciences MathematicsENWeil conjectures 3: Riemann hypothesisRichard E BorcherdsOctober 15, 2020 19 min★ ★ ★ ★ ★ 5/5Weil ConjecturesRiemann HypothesisFinite Fields
Formal & Physical Sciences MathematicsENAlgebraic geometry 37: Singular points (replacement video)Richard E BorcherdsOctober 14, 2020 20 min★ ★ ★ ★ ★ 5/5Algebraic GeometrySingular PointsTangent Space
Formal & Physical Sciences MathematicsENWeil conjectures 2: Functional equationRichard E BorcherdsOctober 13, 2020 20 min★ ★ ★ ★ ★ 5/5Weil ConjecturesFunctional EquationRiemann-Roch
Formal & Physical Sciences MathematicsENCommutative algebra 40 The Eilenberg Mazur swindleRichard E BorcherdsOctober 12, 2020 16 min★ ★ ★ ★ ☆ 4/5Commutative AlgebraEilenberg-Mazur SwindleStably Free Modules
Formal & Physical Sciences MathematicsENAlgebraic geometry 38: The Zariski tangent space (replacement)Richard E BorcherdsOctober 11, 2020 22 min★ ★ ★ ★ ★ 5/5Algebraic GeometryZariski Tangent SpaceLocal Rings
Formal & Physical Sciences MathematicsENCommutative algebra 39 (Stably free modules)Richard E BorcherdsOctober 10, 2020 24 min★ ★ ★ ★ ☆ 4/5Commutative AlgebraStably Free ModulesProjective Modules
Formal & Physical Sciences MathematicsENWeil conjectures 1 IntroductionRichard E BorcherdsOctober 8, 2020 34 min★ ★ ★ ★ ★ 5/5Weil ConjecturesRiemann HypothesisZeta Functions
Formal & Physical Sciences MathematicsENCommutative algebra 37 Blowup algebrasRichard E BorcherdsOctober 7, 2020 22 min★ ★ ★ ★ ★ 5/5Commutative AlgebraBlowup AlgebrasRees Algebra
Formal & Physical Sciences MathematicsENRiemann Roch. Proof (part 2)Richard E BorcherdsOctober 6, 2020 27 min★ ★ ★ ★ ★ 5/5Riemann-RochSerre DualityAlgebraic Geometry
Formal & Physical Sciences MathematicsENCommutative algebra 36 Artin Rees lemmaRichard E BorcherdsOctober 5, 2020 18 min★ ★ ★ ★ ★ 5/5Commutative AlgebraArtin-Rees LemmaNoetherian Rings
Formal & Physical Sciences MathematicsENCommutative algebra 35 Nakayama's lemmaRichard E BorcherdsOctober 4, 2020 17 min★ ★ ★ ★ ★ 5/5Nakayama's LemmaCommutative AlgebraLocal Rings
Formal & Physical Sciences MathematicsENCommutative algebra 34 Geometry of normalizationsRichard E BorcherdsOctober 3, 2020 23 min★ ★ ★ ★ ★ 5/5Commutative AlgebraAlgebraic GeometryNormalization
Formal & Physical Sciences MathematicsENRiemann Roch: Proof, part 1Richard E BorcherdsOctober 1, 2020 29 min★ ★ ★ ★ ★ 5/5Riemann-Roch TheoremAlgebraic GeometryDivisors
Formal & Physical Sciences MathematicsENRiemann Roch: plane curvesRichard E BorcherdsSeptember 29, 2020 23 min★ ★ ★ ★ ★ 5/5Riemann-RochPlane CurvesGenus
Formal & Physical Sciences MathematicsENRiemann Roch: genus 3 curvesRichard E BorcherdsSeptember 24, 2020 30 min★ ★ ★ ★ ★ 5/5Riemann-RochGenus 3Algebraic Curves
Formal & Physical Sciences MathematicsENRiemann Roch: genus 2 curvesRichard E BorcherdsSeptember 21, 2020 30 min★ ★ ★ ★ ★ 5/5Riemann-Roch TheoremGenus 2 CurvesHyperelliptic Curves
Formal & Physical Sciences MathematicsENRepresentation theory: Burnside's theoremRichard E BorcherdsSeptember 21, 2020 17 min★ ★ ★ ★ ★ 5/5Burnside's TheoremRepresentation TheoryGroup Theory
Formal & Physical Sciences MathematicsENRiemann Roch: structure of genus 1 curvesRichard E BorcherdsSeptember 17, 2020 18 min★ ★ ★ ★ ★ 5/5Riemann-RochGenus 1Elliptic Curve
Formal & Physical Sciences MathematicsENIntroduction to Diophantine equationsRichard E BorcherdsSeptember 15, 2020 39 min★ ★ ★ ★ ★ 5/5Diophantine EquationsNumber TheoryAlgebraic Geometry
Formal & Physical Sciences MathematicsENRiemann Roch: genus 1Richard E BorcherdsSeptember 14, 2020 31 min★ ★ ★ ★ ★ 5/5Riemann-RochElliptic CurvesAlgebraic Geometry
Formal & Physical Sciences MathematicsENRepresentation theory: The Schur indicatorRichard E BorcherdsSeptember 12, 2020 22 min★ ★ ★ ★ ★ 5/5Schur IndicatorRepresentation TheoryBilinear Forms
Formal & Physical Sciences MathematicsENRepresentation theory: Examples D8, A4, S4, S5, A5Richard E BorcherdsSeptember 11, 2020 23 min★ ★ ★ ★ ★ 5/5Representation TheoryCharacter TablesFinite Groups
Formal & Physical Sciences MathematicsENRiemann Roch for genus 0 curvesRichard E BorcherdsSeptember 9, 2020 21 min★ ★ ★ ★ ★ 5/5Riemann-RochGenus 0Algebraic Geometry
Formal & Physical Sciences MathematicsENRepresentation theory: Orthogonality relationsRichard E BorcherdsSeptember 9, 2020 25 min★ ★ ★ ★ ★ 5/5Representation TheoryOrthogonality RelationsCharacter Table
Formal & Physical Sciences MathematicsENRepresentation theory: Dirichlet's theoremRichard E BorcherdsSeptember 8, 2020 22 min★ ★ ★ ★ ★ 5/5Dirichlet's TheoremRepresentation TheoryCharacters