RLM 8.136

The Derived Algebraic Geometry seminar meets every **Wednesday** at
**4pm** (and occasionally Friday), in **RLM 8.136**. (Check the schedule below for exact dates.)

This is a learning seminar organized by Richard Hughes (rhughes [at] math [dot] utexas [dot] edu) and Aaron Royer. It it the continuation of a Fall 2014 seminar on Rational Homotopy Theory, which was organised by Dan Kaplan.

This aim of this seminar is to study derived algebraic geometry, with a focus on understanding Jacob Lurie's work on formal moduli problems (DAG X). A list of references organized by topic can be found below.

The schedule of talks is as follows:

Date | Topic | Speaker | Selected References |
---|---|---|---|

28th January | Examples of moduli problems | Richard Hughes | [BZ] [F] [L2] |

4th February | Formal algebraic geometry and completion | Dan Kaplan | [H] [S] |

11th February | What is a stack? | Rustam Antia-Riedel | [B] [F] |

13th February | What is a higher stack? (Friday overflow discussion) |
Group discussion | [T1] |

18th February | Infinity categories as models for homotopy theories | Yaoguang Zhu | [L3] [L4] |

25th February | Category theory of infinity categories | Yuri Sulyma | [G] [L4] |

27th February | More homotopy and category theory for infinity categories (Friday overflow discussion) |
Group discussion | [G] [L3] [L4] |

4th March | Algebra in infinity categories | Val Zakharevich | [L5] |

11th March | Cotangent complex formalism | Yuecheng Zhu and Tom Mainiero | [F] [L2] [L5] [LV] [PV] [Q] [V] |

13rd March | More on the cotangent complex (Friday overflow) |
Yuecheng Zhu | [PV] [Q] [V] |

18th March | Spring Break |
Nobody (take a holiday, folks) |
Read a good novel (and DAG-X!) |

25th March | What is a formal derived stack? | Yuecheng Zhu and Tom Mainiero | [F] [L2] [PV] [V] |

1st April | Introduction to DAG-X | Surya Raghavendran | [L1] |

8th April | The deformation context of commutative algebras | Yuri Sulmya | [L1] |

15th April | dg-Lie algebras and the tangent complex | Rustam Antia-Riedel | [L1] [L5] |

17th April | Lie algebras (Friday overflow discussion) |
Rustam Antia-Riedel | [L1] [L5] |

22nd April | Deformation theories | Aaron Royer | [L1] [L5] |

29th April | No seminar |
||

8th May | Koszul duality is a deformation theory | Richard Hughes | [L1] [L5] |

- [L1] Lurie, DAG X.
- [L2] Lurie, Moduli problems for ring spectra (ICM address).

- [H] Hartshorne, Algebraic Geometry, Ch 2.9.
- [S] Strickland, Formal schemes and formal groups.

- [G] Groth, A short course on infinity categories.
- [L3] Lurie, What is an... Infinity Category?
- [L4] Lurie, Higher Topos Theory, (Chapters 1, 2, 3).
- [R] Riehl, Quasi-category theory you can use (talk at GSTGC 2014).

- [Q] Quillen, On the (co)homology of commutative rings.
- [L5] Lurie, Higher Algebra, Chapter 7.3 and 7.4.
- [PV] Porta and Vezzosi, Infinitesimal and square-zero extensions of simplicial algebras.
- [V] Vezzosi, A note on the cotangent complex in derived algebraic geometry.

- [BZ] Ben-Zvi, Moduli Spaces.
- [B] Brambila-Paz, et al, Moduli Spaces, Chapter 1 (Kai Behrend, "Introduction to algebraic stacks").
- [F] Fantechi, et al, Fundamental Algebraic Geometry: Grothendieck’s FGA Explained, Chapter 6.

- [LV] Loday and Vallette, Algebraic Operads.
- [Fr] Francis, The tangent complex and Hochschild cohomology of E_n-rings.