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 :)
General information
For instructions and guidelines for the speakers, see below.
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.
Program
You can find the pdf file of the program here.
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 | Chenyi Yang | Line bundles, linear systems, divisors, maps to projective spaces |
| 12:00–13:30 | –/–/– | Lunch break | |
| 13:30–15:30 | 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 | 10:00–12:00 | Yiming Wang | Riemann–Hurwitz formula: the Lüroth’s theorem, endomorphisms of curves of genus \(g>1\) |
| 12:00–13:30 | –/–/– | Lunch break | |
| 13:30–15:30 | Anjali Paul | Belyi’s theorem and dessins d’enfants | |
| 15:30–16:00 | –/–/– | Coffee break | |
| 16:00–18:00 | Lei Kuang | Cubic curves: construction of the group law | |
| 08.10 | 13:30–15:30 | 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 | Bo–Jacopo | Cohomology, Riemann–Roch, and Serre Duality – 1 |
| 13:00–14:30 | –/–/– | Lunch break | |
| 14:30–16:30 | Jacopo–Bo | Cohomology, Riemann–Roch, and Serre Duality – 2 |
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
Let’s start with the most important point.
- Don’t hesitate to ask questions about your talk/surrounding math at any point in time! Also, please ask questions during the talks of other participants!
We also collected some thoughts on how to prepare and give a talk, and how we will grade the reports of the talk. For extra suggestions, we suggest reading the advice for talks. We think that giving talks is a hard art-form to master, but we hope this advice can be of help :)
Talk preparation
During the preparation of your talk, please keep in mind the following.
- The main aim of the talk is to make the audience understand.
- The program is a guideline in the following sense. You should prioritize points that are not marked by * and you might have to complement what is written with extra material in order to get a coherent explanation.
Let’s see what this entails more in detail.
- Reach out if it is not clear what’s meant in the program.
- Try to include examples, motivations (and your own interpretation!) aimed at clarifying the objects you are asked to introduce.
- If you think your talk is too short, don’t worry. Your main task is to work on the quality of the explanation, not on the quantity of the material (that is up to us!). If you still want to add material, see the previous point.
Giving the talk
Take questions from the audience seriously.
Pause your talk to understand the question. Once you understand it, try to rephrase it to check if your understanding is correct. If you don’t know how to answer, you should honestly admit that. (maybe another person will provide an answer!)
IMPORTANT: Your answers during the talk will not affect your grade.
Do not rush your explanation!
If you realize you are running out of time, it’s better to cut some material out than to rush through it. You can ask the organizers for suggestions on what to skip, but it’s a good idea to think about it already during the preparation phase of the talk.
Grading of the report
While grading the report, we will adhere to the following. We think it might be useful to share these with you.
- The report should represent the speaker’s understanding of the material rather than somebody else’s. Practically, the report should be written by the speaker and no parts should be copied from the sources.
- The report should reflect the content of the talk (more explicitly, the order of the presented material, inclusion/omission of proofs and examples). Big deviations from the talk will not be corrected. There may be more material in the report, but only in the direction of more clarification of the presented material: there can be more details to some proofs, more details of some examples, slightly more general hypotheses of the statements, etc.
- If during the talk some questions come up, answers to which should be beneficial for the understanding of the material, the answers should be included in the report. Feel free to contact us about each particular question.