General information
Important!
The program is now complete and all talks are taken. However, everyone is welcome to attend the seminar. (Note that it takes place before the semester starts!) We hope to see you there :)
Time and Place
5 – 9 October in room M 102
Description
The seminar aims to introduce several fundamental methods and tools of algebraic geometry through the study of algebraic curves.
Instructions
Please try to you adhere to the following for the preparation of the talk.
- Prepare at least a preliminary plan of the talk by mid-September at the latest and communicate it to us.
- Have a meeting with one of us when your talk is almost ready, at the latest one week before your talk (e.g. for the talks on the first day, you should meet us before the 25.09). The meeting can also be online if needed.
- To receive a grade for the seminar, you have to hand in a report covering the content of your talk. The final report has to be submitted by the end of the winter semester, preferably by the end of December.
Guidelines
Here are some guidelines for the preparation of the talk itself.
- Don’t hesitate to ask questions about your talk/surrounding math at any point in time! (In particular, ask if it’s not clear what’s meant in the program.)
- The program is a guideline in the following sense. What’s written there should all be included in the talk (apart potentially for *-marked points), but you might have to include more material for a coherent talk. This is part of the tasks of preparing a seminar talk!
- The provided references are meant to help with point 2, but you might find it useful to look for other references too.
- We suggest reading the advice for talks. Giving talks is a hard art-form to master, therefore we collected some advice that we hope can be of help :) (On this note, keep in mind that only the report is officially graded; we hope that not having to stress about the grade can help you focus on the talk itself!)
Links
Schedule
Important!
The following schedule is preliminary
| Day | Time | Speaker | Content |
|---|---|---|---|
| 05.10 | 11:00–13:00 | Sebastian Rohr | Local structure of smooth curves, maps between curves |
| 13:00–14:30 | –/–/– | Lunch break | |
| 14:30–16:30 | Shi Dong | Closed points of smooth projective curves and dominant morphisms between curves | |
| 06.10 | 10:00–12:00 | Pavel Sechin | Line bundles, linear systems, divisors, maps to projective spaces |
| 12:00–13:30 | –/–/– | Lunch break | |
| 13:00–15:30 | Sasha Bonacci | Maps from curves to a projective space and applications of the Riemann–Roch | |
| 15:30–16:00 | –/–/– | Coffee break | |
| 16:00–18:00 | Zihan He | Curves of genus \(0\) | |
| 07.10 | 11:00–13:00 | Yiming Wang | Riemann–Hurwitz formula: the Lüroth’s theorem, endomorphisms of curves of genus \(g>1\) |
| 13:00–14:30 | –/–/– | Lunch break | |
| 14:30–16:30 | Anjali Paul | Belyi’s theorem and dessins d’enfants | |
| 08.10 | 10:00–12:00 | Lei Kuang | Cubic curves: construction of the group law |
| 12:00–13:30 | –/–/– | Lunch break | |
| 13:00–15:30 | Michael Lindner | Elliptic curves: \(j\)-invariant, Jacobian, cohomology | |
| 15:30–16:00 | –/–/– | Coffee break | |
| 16:00–18:00 | Sara Donè | Jacobians of algebraic curves | |
| 09.10 | 11:00–13:00 | Aditya–Jacopo | Cohomology, Riemann–Roch, and Serre Duality – 1 |
| 13:00–14:30 | –/–/– | Lunch break | |
| 14:30–16:30 | Jacopo–Aditya | Cohomology, Riemann–Roch, and Serre Duality – 2 |