Welcome to the seminar MAT716 on Differentiable Stacks!

Topics

• - Lie groupoids and Lie algebroids [1 §1.1, 3]
  
  • • Definition
    • Examples
    • Properties
• - Morita equivalence and differentiable stacks [1 §1.2, 2 §2]
  
  • • Leaf spaces
    • Atlases
    • Basic examples
• - Examples of stacks [2 §3]
  
  • • Moduli stack of triangles
    • Classifying stack of a group 
    • Cech groupoid and gluing data
• - Differential forms and shifted symplectic structures [2 §4-5]
• - Cohomology theory of simplicial spaces [1 §1.3]
• - Categorical definition of stacks [1, §1.2.6, 2 §1, 7]
• - Gerbes as Stacks [2 §6, 4]

Sources

[1] Ping Xu 2017, Differentiable Stacks, Gerbes, and Twisted K-Theory

[2] Grégory Ginot 2013, Introduction to Differentiable Stacks

[3] Eckhard Meinrenken 2017, LIE GROUPOIDS AND LIE ALGEBROIDS LECTURE NOTES

[4] Nigel Hitchin 1999, LECTURES ON SPECIAL LAGRANGIAN SUBMANIFOLDS

[5] Henrique Bursztyn 2024, Slides from Poisson conference 2024

[6] Kai Behrend, Ping Xu 2008, Differentiable Stacks and Gerbes

[7] Barbara Fantechi, Stacks for Everybody

Evaluation

Pass/fail based on a presentation with latex notes and participation during talks.

Module: 

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