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.
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|
|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|
|Lecture 12: Lagrangians and Lagrangian fibrations||Video|
|3/26/2019||Lecture 13: Intersections of Lagrangians||Video|
|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|
|Lecture 17: Uhlenbeck–Yau construction and correspondence Examples (Part I)||Video|