Hodge theory is a beautiful and powerful subject, and the algebraic geometry prerequisites are minimal.
We will follow Voisin's book, Hodge Theory and Complex Algebraic Geometry I. It is available in electronic form via the University of Liverpool library website.
This is intended as a friendly learning seminar; we will take the time to introduce the foundational material and discuss examples. I have a timeline for the first part of the seminar, but feel free to put forward suggestions for additional topics. Everybody is welcome!
The seminar will be held virtually on Teams. The team name is "Working seminar on Hodge theory". Please email me if you need the team link.
Schedule: Wednesday 4-5pm
First talk: April 22, 2020
Tentative Schedule: (also availabe on the Liverpool algebraic geometry Google calendar)
| Day | Speaker | Title | |
|---|---|---|---|
| 2020 | |||
| April 22 | Alice | Reminder on holomorphic funtions | |
| April 29 | Rhys | Complex manifolds and vector bundles, almost complex structures | |
| May 6 | Sam | del and del bar, the Dolbeaut complex | |
| May 13 | Aeran | Hermitian and Kaehler metrics | |
| May 20 | Thomas | Kaehler metrics and connections, part I | |
| May 27 | Thomas | Kaehler metrics and connections, part II | |
| June 3 | Felix | Cohomology and de Rham theorems | |
| June 10 | Tom | The Hodge decomposition and some consequences | |
| June 17 | Thomas | Proof of the Hodge decomposition theorem, I | |
| June 24 | Thomas | Proof of the Hodge decomposition theorem, II | |
| July 8 | Sam | Examples of Kaehler manifolds | |
| July 15 | Tom | The Hodge decomposition and the Frolicher spectral sequence | |
| July 22 | Felix | The Frolicher spectral sequence collapses | |
| 2021 | |||
| October 14th | Alice | Reminder on what we learned last year | |
| October 21st | Thomas | Families of manifolds | |
| October 28th | Felix | The Kodaira-Spencer map | |
| November 11th | Jon | The Gauss-Manin Connection | |
| November 18th | Rhys | Semicontinuity theorems | |
| May 19th | Marco | Mixed Hodge structures I | |
| May 26th | Marco | Mixed Hodge structures II | |