This is the webpage of the student learning seminar on algebraic geometry at Columbia. The predecessor of this seminar is the Remynar, from which the template for this page is partially copied.

This semester's topic is the Decomposition Theorem of Beilinson-Bernstein-Deligne. The main reference is the survey article [dCM] below, though we will need to consult other references to fill in details. We will assume familiarity with algebraic geometry at the level of Hartshorne, along with some basics of derived categories and étale cohomology.

References:

- [BBD] Beilinson, Bernstein, Deligne, Faisceaux pervers
- [dCM] de Cataldo, Migliorini, The Decomposition Theorem, Perverse Sheaves, and the Topology of Algebraic Maps
- [KW] Kiehl, Weissauer, Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform

Please e-mail the organizers if you'd like to receive notifications.

**Organizers:** Shizhang Li, Carl Lian.

**Time and location:** Tuesday 16:30-18:00 in Math 507

*in addition to the unusual dates, these talk will take place 10:00-11:30 in Math 528.

Date | Speaker | Title | Ref. |
---|---|---|---|

17 Jan | Shizhang Li | Introduction | [dCM] 1 |

24 Jan | Qixiao Ma | Six Functors; Verdier Duality | [dCM] 5.3, 5.8 |

31 Jan | Henry Liu | Intersection Cohomology, I | [dCM] 2.1-2.2 |

7 Feb | Raymond Cheng | Intersection Cohomology, II | [dCM] 2.1-2.2 |

14 Feb | Semon Rezchikov | Perverse Sheaves, I | [dCM] 2.3-2.5, [KW] 3 |

21 Feb | Leonardo Lerer | Perverse Sheaves, II | [dCM] 2.3-2.5, [KW] 3 |

6 Mar* |
David Hansen | Lefschetz Hyperplane Theorem, Intermediate Extensions | [dCM] 2.6-2.7 |

7 Mar | Dmitrii Pirozhkov | Overview of Proof | [dCM] 3.1 |

14 Mar | No talk: Spring break/AWS |
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21 Mar | Dan Gulotta | Semismall Maps | [dCM] 4.2 |

27 Mar* |
Noah Arbesfeld | Gottsche's Formula | |

4 Apr | Cancelled |
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11 Apr | David Hansen | Geometric Satake Isomorphism | |

18 Apr | Daniel Litt | The P=W Conjecture | |

25 Apr | Shizhang Li | On Bhatt-Schnell-Scholze |