Exchange Seminar

This is the schedule of second part of the Exchange seminar, organised together with Yuan Yao. The website of the first part can be found here.

Aim: Learn about virtual fundamental classes and global Kuranishi charts and their applications
Format: We read (some of) the references beforehand and then discuss. The meetings are hybrid. (Write me or Yuan an email if you want to join.)
Time: The exact meeting time will be communicated via mail.

• Meeting 1: basic definitions of orbifolds in terms of groupoids
  • Orbifolds as groupoids §1-3
  • Orbifolds and Stringy Topology, Chapter 1
    
• Meeting 2: orbibundles, orbisections and a bit of orbifold cohomology
  • Orbifolds as groupoids §4-6
  • On orbifold embeddings
  • Cohomology of stacks
    
• Meeting 3 (8.1.): moduli spaces of stable curves and their orbifold structures
  • A construction of the Deligne-Mumford orbifold
  • Geometry of algebraic curves Volume II, §XI.3-5, §XII.4,10
  • Moduli of curves
    
• Meeting 4 (17.1.): i) global Kuranishi charts and vfc
  ii) discussion of toy cases (come up with your favourite example beforehand)
  • Complex cobordism, Hamiltonian loops and global Kuranishi charts, §4.1 and 5.1
  • Properties of Gromov-Witten invariants defined via global Kuranishi charts, §A
    
• Meeting 5 (14.2.): discussion of the topic of last meeting and of examples
  
• Meeting 6 (28.2.) global Kuranishi charts for moduli spaces of stable pseudoholomorphic maps
  • Complex cobordism, Hamiltonian loops and global Kuranishi charts, §6
  • Gromov-Witten invariants in complex-oriented generalised cohomology theories
  • Global Kuranishi charts and a product formula in symplectic GW theory
    
• Week of the 11th of March: Minicourse by Shaoyun Bai on global Kuranishi charts for Hamiltonian Floer theory
  • Arnol’d conjecture over the integers
    
• Meeting 8 (27.3.) same topic as meeting 7
  
• Meeting 9 (3.4.) talk by Russell Avdek on the semi-global Kuranishi charts of Bao-Honda
  
• Meeting 10 (19.4.) parametrised and equivariant global Kuranishi charts
  • Properties of Gromov-Witten invariants defined via global Kuranishi charts, §5