Monday | Wednesday | Friday |
---|---|---|

August 26
No class | August 28
No class. Math classes numbered 500 and above do not meet before September 3. | August 30
No class. Math classes numbered 500 and above do not meet before September 3. |

September 2
No class: Math classes numbered 500 and above do not meet before September 3. | September 4
In Lecture - Definition of a group, basic examples
- Subgroups, homomorphisms, normal subgroups, quotient groups, exact sequences
- Permutation groups, operations of groups on sets
- The origin of group theory in Galois Theory
- The orbit formula
Associated Reading: - D-F: 1.1, 1.2, 1.4, 1.6, 1.7, 2.1
- Lang: 1.1 - 1.5
Video of class (downloadable) | September 6
No Class. |

September 9
Lecture - The orbit formula, continued
- The class equation
- Sylow theorems
- Symmetric groups and isometry groups
Associated Reading: - D-F: 1.2, 1.3, 4.3, 4.5
- Lang: 1.5, 1.6,
Video of class (downloadable) | September 11
Lecture - Proof of the Sylow theorems
- Applications of the Sylow theorems
Associated Reading: - D-F: 1.2, 1.3, 2.5, 3.4, 4.3, 4.5
- Lang: 1.3, 1.4, 1.5, 1.6
- An article by Howard Hiller about crystallography
Video of class (downloadable) | September13
Lecture (In room 4C8 of DRL labs, 9:00 - 10:30) - Applications of the Sylow theorems, continued
- Semi-direct products
Associated Reading: - D-F: 1.2, 1.3, 2.5, 3.4, 4.3, 4.5
- Lang: 1.3, 1.4, 1.5, 1.6
Video of class (downloadable) |

September 16
Lecture - Topological groups
- Quotients of topological spaces by group actions
- Crystallographic groups
Associated Reading: - D-F: 2.5, 3.4, 4.3, 4.4, 4.5
- Lang: 1.3, 1.4, 1.5, 1.6
- An article by Howard Hiller about crystallography
Video of class (downloadable) | September 18
Lecture - Schreier's Theorem
- Jordan Holder Theorem
- Classifying finite simple groups
Associated Reading: - D-F: 2.5, 3.4, 4.3, 4.4, 4.5
- Lang: 1.3, 1.4, 1.5, 1.6
Video of class (downloadable) | September 20
No class |

Sept. 23
In Lecture - Derived series, lower and upper central series
- Nilpotent groups
Associated Reading: - D-F: 2.5, 3.4, 4.3, 4.4, 4.5
- Lang: 1.3, 1.4, 1.5, 1.6
Video of class (downloadable) | Sept. 25
In Lecture: - Nilpotent groups, continued
- The Frattini argument
Associated Reading: Video of class (downloadable) | Sept. 27
No class |

Sept. 30
In Lecture - Multiply transitive groups
- Blocks and primitive groups
- The group extension problem and H^2
Associated Reading: - "Finite permutation groups" by H. Wielandt.
- D-F: 2.5, 3.4, 4.3, 4.4, 4.5 , 17.4
- Lang: 1.3, 1.4, 1.5, 1.6
Video of class (downloadable) | Oct. 2
In Lecture: - The group extension problem and H^2
Associated Reading: - D-F: 17.4
Video of class (downloadable) | Oct. 4
In Lecture: Room 4C8 of DRL labs, 9:00 - 10:30 - The group extension problem and H^2, continued
- Start of Category theory
Associated Reading: - D-F: 17.4
- D-F: 2.5, 3.4, 4.3, 4.4, 4.5, 5.2, Appendix II, 6.3
- Lang: 1.3, 1.4, 1.5, 1.6, I.8, I.11, I.12
Video of class (downloadable) |

Oct. 7
In Lecture (room 4N30 of DRL): - Category theory and applications
- Natural tranformations
- Automorphisms of functors
Associated Reading: - D-F: Appendix II, 6.3
- Lang: I.11, I.12
Video of class (downloadable) | Oct. 9
In Lecture: - The category of rings
- Representations of groups
- Representability of the functor associated to representations of a group over a ring
Associated Reading: - Lang, II.1 - II.3, Appendix 2.2.
- Dummit and Foote, 7.1 - 7.4, Appendix I.
- Dummit and Foote, chapter 18.1
- Pages 313 - 318 of This article by Lenstra and de Smit on deformation rings.
Video of class (downloadable) | Oct. 11
No class |

Oct. 14
In Lecture (room 4N30 of DRL): - Products and coproducts
- Pullback and pushouts
Associated Reading: - D-F: Appendix II, 6.3
- Lang: I.11, I.12
Video of class (downloadable) | Oct. 16
In Lecture: - Pullback and pushouts, continued
- Free groups, groups defined by generators and relations
Associated Reading: - D-F: Appendix II, 6.3
- Lang: I.11, I.12
Video of class (downloadable) | Oct. 18
No class |

Oct. 21
In Lecture (room 4C8 of DRL): - The Todd Coxeter algorithm
Associated Reading: - This Wikipedia entry about the Todd Coxeter algorithm.
Video of class (downloadable) | Oct. 23
No class | Oct. 25
In Lecture (room 4C8 of DRL from 9:00 to 10:30): - Fundamental groups and the Van Kampen Theorem
Associated Reading: - This Wikipedia entry about the Van Kampen theorem.
Video of class (downloadable) |

Oct. 28
In Lecture (room 4C8 of DRL): - Representable moduli problems
- Principal G-bundles
- Families of elliptic curves
- Coarse moduli spaces
Associated Reading: - This Wikipedia entry about principal G-bundles.
- This Wikipedia entry about coarse moduli spaces.
- This Wikipedia entry about complex elliptic curves
Video of class (downloadable) | Oct. 30
In Lecture (room 4C8 of DRL): - More on the Todd Coxeter algorithm
- Vector bundles
Associated Reading: - This Wikipedia entry on vector bundles.
- This Wikipedia entry about complex elliptic curves
- This Wikipedia entry about the Todd Coxeter algorithm.
Todd Coxeter Recap Video (downloadable) Vector bundle video (downloadable) | Nov.1
No class |

Nov. 4
In Lecture (room 4C8 of DRL): - Another construction of vector bundles by group theory
- Cocyles and local trivializations
Associated Reading: - This Wikipedia entry on vector bundles.
Video of class (downloadable) | Nov. 6
In Lecture (room 4C8 of DRL): - Direct and inverse limits in categories
- P-Adic numbers
Associated Reading: - D-F: 5.2
- Lang: I.8, 1.10.
Video of class (downloadable) | Nov. 8
No class |

Nov. 11
No class | Nov. 13
In Lecture (room 4C8 of DRL): - Abelian categories
- Injectives and projectiles
- Derived functors
Associated Reading: - Section III.1 of Hartshorne's ``Algebraic Geometry".
- Lang, XX.6 - XX.7.
- Serre, Corps Locaux, on group cohomology
Video of class (downloadable) | Nov. 15
In Lecture (room 4C8 of DRL at 9:00 a.m.): - Derived functors, continued
- Cohomology of groups
- Presheaves and sheaves
Associated Reading: - Section II.1, III.1 of Hartshorne's ``Algebraic Geometry".
- Lang, XX.6 - XX.7.
- Serre, Corps Locaux, on group cohomology
Video of class (downloadable) |

Nov. 18
No class | Nov. 20
No class | Nov. 22
No class |

Nov. 25
No class | Nov. 27
No class | Nov. 29
No class |

Dec. 2
In Lecture: - Ext groups and Derived functors, continued
- Cohomology of groups
Associated Reading: - Section II.1, III.1 of Hartshorne's ``Algebraic Geometry".
- Lang, XX.6 - XX.7.
- Serre, Corps Locaux, on group cohomology
Video of class (downloadable) | Dec. 4
In Lecture (room 4C8 of DRL): - Presheaves and sheaves
- Sheaf cohomology
Associated Reading: - Section III.1 of Hartshorne's ``Algebraic Geometry".
- Lang, XX.6 - XX.7.
Video of class (downloadable) | Dec. 6
In Lecture (room 4C8 of DRL at 9:00 a.m.): - Betti homology and cohomology of simplicial complexes
- Ring theory: basic definitions
- Principal ideal domains
- Maximal and prime ideals
Associated Reading: - Lang, XII.6, II.5,
- DF, p. 232, 8.2, 8.3
Video of class (downloadable) |

Dec. 9
In Lecture: - Spectrum of a ring
- Localization
Associated Reading: - Lang, XII.6, II.5,
- DF, p. 232, 8.2, 8.3
Video of class (downloadable) | Dec. 11
In Lecture (room 4C8 of DRL): - Chinese remainder Theorem
- Euclidean rings
- Principal ideal domains
Associated Reading: - Lang, XII.6, II.5,
- DF, p. 232, 8.2, 8.3
Video of class (downloadable) | Dec. 13
In Lecture (room 4E18 of DRL at 9:00 a.m.): - Principal ideal domains and Euclidean rings (continued)
- Valuations and discrete valuation rings
- Unique factorization domains
Associated Reading: - Lang, XII.6, II.5,
- DF, p. 232, 8.2, 8.3
Video of class (downloadable) |

Last updated: 12/7/13

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