In the Spring 2019 Semester, the CMSA will be hosting a special lecture series on** Derived algebraic/differential geometry** run by Artan Sheshmani, with lectures given by Prof. Sheshmani and Dr. Dennis Borisov. The seminar will be held on **Tuesdays and Thursdays from 3:00-4:30pm** in **CMSA, room G10.**

**Click here for reference material**

**Section 1: Basic setting of derived geometry**

The goal: To collect the minimum set of tools needed to do algebraic geometry in the derived context.

2/05/2019 | Lecture 1: Model and с-categories | |

2/07/2019 | Lecture 2: Grothendieck topologies and homotopy descent | |

2/12/2019 | Lecture 3: Derived Artin stacks | |

2/14/2019 | Lecture 4: Cotangent complexes |

**Section 2: Loop spaces and differential forms**

The goal: This is the algebraic heart of the course – here we learn the homological techniques that are needed for shifted symplectic forms.

2/19/2019 | Lecture 5: De Rham complexes and S1-equivariant schemes (loop spaces) | |

2/21/2019 | Lecture 6: Chern character | |

2/26/2019 | Lectures 7: Local structure of closed differential forms in the derived sense Part I | |

2/28/2019 | Lectures 8: Local structure of closed differential forms in the derived sense Part II | |

3/05/2019 | Lecture 9: Cyclic homology |

**Section 3: Shifted symplectic structures**

Goal: To see applications of the algebraic techniques from above in the geometric context of the actual moduli spaces.

3/07/2019 | Lecture 10: Definition and existence results | |

3/12/2019 | Lectures 11: Lagrangians and Lagrangian fibrations | |

3/14/2019 | Lectures 12: Lagrangians and Lagrangian fibrations | |

3/19/2018 | Lecture 13: Intersections of Lagrangians | |

3/21/2019 | Lecture 14: Examples and applications 2 (Part I) | |

3/26/2019 | Lecture 15: Examples and applications 2 (Part II) |

**Section 4: Uhlenbeck–Yau construction and correspondence**

3/28/2019 | Lecture 16 TBA | |

4/02/2019 | Lecture 17 TBA | |

4/04/2019 | Lecture 18 TBA |