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.

VIDEO Click here for reference material

Click here for a syllabus

Schedule:
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
Video
2/07/2019
Lecture 2: Grothendieck topologies and homotopy descent
Video
2/12/2019
Lecture 3: Derived Artin stacks
Video
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)
Video
2/21/2019
Lecture 6: Chern character
Video
2/26/2019

Room G02

Lecture 7: Local structure of closed differential forms in the derived sense Part I
Video
2/28/2019
Lecture 8: Local structure of closed differential forms in the derived sense Part II
Video
3/05/2019
Lecture 9: Cyclic homology
Video

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
Video
3/12/2019
Lecture 11: Lagrangians and Lagrangian fibrations
Video
3/14/2019

Room G02

Lecture 12: Lagrangians and Lagrangian fibrations
Video
3/26/2019
Lecture 13: Intersections of Lagrangians
Video
3/28/2019

Room G02

Lecture 14: Examples and applications 2 (Part I)
Video
4/02/2019
Lecture 15: Examples and applications 2 (Part II)
Video

Section 4: Uhlenbeck–Yau construction and correspondence

4/04/2019
Lecture 16: Examples and applications 2 (Part III)
Video
4/09/2019

Room G02

Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)
Video