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|
|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|
|4/06/2019||Lecture 18 TBA|