2026 Fall
Mixed Hodge Structures
On the fundations of Deligne's mixed Hodge structures
Description
The goal of this seminar is to cover the basic definitions of mixed Hodge structures as well as its construction on general varieties, with an emphasis on concrete examples. If time allows, we could also investigate mixed Hodge structures on degenerations and/or explicit study of mixed Hodge structures on moduli spaces.
Spacetime
Weekly on Friday 3:30-5:00, Evans 762.
References
- [PS] Mixed Hodge Structures by Peters and Steenbrink, our main reference for this seminar
- [Co] Cohomological Descent by Brian Conrad
- [De] Théorie de Hodge : III by Pierre Deligne
Tentative Schedule
| Week | Date | Topic | Reference | Speaker | Notes |
|---|---|---|---|---|---|
| 2 | 9/1 | Organization and short review on Hodge theory | Chap 1 | Xiangru Zeng | |
| 3 | 9/11 | Pure Hodge structures | 2.1-2.3 | Cameron Chang | |
| 4 | 9/18 | Mixed Hodge structures | 3.1-3.4 | Pranav Enugandla | |
| 5 | 9/25 | Mixed Hodge theory for smooth varieties | 4.1-4.4+some parts of 4.5 | Xiangru Zeng | SVG |
| 6 | 10/2 | Cohomologial descent | 5.1-5.2, also see [Co] | Michael R. Zeng | |
| 7 | 10/9 | Mixed Hodge structures for singular varieties | 5.3-5.5 | Cameron Chang | |
| 8 | Skip | ||||
| 9 | TBD | ||||
| 10 | Skip | ||||
| 11 | TBD | ||||
| 12 | TBD | ||||
| 13 | TBD | ||||
| 14 | TBD |
