git & nahc
This is where Enya Hsiao and I organise the Geometric Invariant Theory & Non-abelian Hodge Correspondence Reading Seminar.
Here is the current version of the seminar plan!
Update 2024-04-09: Final update, all notes uploaded! Thank you all for participating!
The nonabelian Hodge correspondence is a deep and beautiful theory that identifies three moduli spaces: the Betti moduli space
The goal of this reading seminar is two-fold:
- Understand the workings of geometric invariant theory and how they are applied in the construction of the moduli spaces involved in the nonabelian Hodge correspondence.
- Understand the geometric properties of objects in the moduli spaces and without going into too much nasty detail, sketch the correspondence between the moduli spaces for
.
Schedule
Date | Topic | Speaker | |
---|---|---|---|
16.11. | 0. | Introduction and overview | |
23.11. | 1. | Affine and projective varieties | Leonie |
30.11. | 2. | Algebraic groups and invariant theory | Barbara |
07.12. | 3. | Affine GIT | Anaëlle |
14.12. | D1. | Discussion: Gauge Theory | Merik |
21.12. | ❄️ | ||
28.12. | ❄️ | ||
04.01. | ❄️ | ||
11.01. | 4. | The Betti Moduli space: Character variety | Fernando |
18.01. | 5. | The de Rham Moduli space: Flat connections | Jiajun |
25.01. | 6. | The Riemann-Hilbert correspondence | Pengfei |
02.02. | D2. | Discussion: Proj and Ample line bundles 14:00 | Bernhard |
08.02. | 7. | Projective GIT | Bernhard |
15.02. | 8. | Hilbert-Mumford criterion | Maximilian |
22.02. | 9. | The moduli problem | Leonie |
04.03. | D3. | Discussion: Complex geometry 11:00 | Enya |
07.03. | 🏕️ | ||
14.03. | 10. | The Dolbeault Moduli space: Higgs bundles Room E2 10 | Tim |
21.03. | 11. | Harmonic bundles and Donaldson-Corlette correspondence | Christian |
28.03. | 12. | The Hitchin-Simpson correspondence | Enya |
04.04. | D4. | Discussion: The rank one case | Enya & Tim |