Objectives of the seminar
On the presentations
1. Each presentation should be meticulously prepared, not only by the speaker, but also by the audience (in order to understand the talk).
2. Because of the time limit, you have to tailor the contents. Focus on the most central and essential ideas and leave out the secondary stuffs.
3. Definitions and theorems should always be stated clearly, precisely, and concisely.
4. Do not try to give all the details of a proof unless it involves useful techniques or it is very interesting. Just sketch the main line of thought.
5. Be prepared to answer and discuss any question posed by the audience.
6. For effective learning, English should be used as much as possible, at least for the blackboard writing. Most high-quality math resourses are in English.