Student Symplectic Seminar: Fall 2022

This semester, Shuhao Li and I are organizing a seminar focused on Weinstein domains and their symplectic invariants with the goal of understanding how to do computations. We meet Fridays, 10:30 am -12 pm, in Math Tower 5-127. The main references are by Bourgeois-Ekholm-Eliashberg:

• Effect of Legendrian Surgery (BEE1)
  
• Symplectic homology product via Legendrian surgery (BEE2)

Resources for Legendrian Surgery:

• "Introduction to Legendrian knots and Legendrian contact homology" - Ghiggini
• "Legendrian contact homology in R^3" - Etnyre-Ng
• "Invariants of Legendrian Links" - Ng
• "Computable Legendrian Invariants" - Ng
  

Other useful resources:

• "Weinstein Manifolds Revisited" - Eliashberg
• "From Stein to Weinstein and Back" - Cieliebak-Eliashberg
• "A survey of Floer homology for manifolds with contact type boundary or Symplectic homology" - Oancea
• "A biased view of symplectic cohomology" - Seidel
• Fukaya Categories and Picard-Lefschetz Theory - Seidel
• "A beginner's introduction to Fukaya categories" - Auroux
• Lectures by Dimitroglou Rizell and Ekholm
• Minicourse by Ekholm
  

List of topics

1. Weinstein domains and handlebody calculus; notes by Shuhao (posted with permission)
2. Symplectic cohomology; my notes
3. Wrapped Fukaya category and A_\infty structure
4. Chekanov-Eliashberg DGA and Legendrian Surgery
5. More Legendrian Surgery and set up for BEE1
6. Linear contact homology and (reduced) symplectic cohomology (BEE1)
7. Legendrian exact triangle and applications (BEE1)
8. Product structure (BEE2)
9. BV structure (BEE2)