Special Lecture Series on Derived Algebraic/Differential Geometry

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 BorisovThe seminar will be held on Tuesdays and Thursdays from 3:00-4:30pm in CMSA, room G10.

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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
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

 

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