Rob's homepage - Topics in 4-manifolds

Topics in 4-manifolds. Seminar course coteached with Laura Wakelin. Summer semester 2024.

Download syllabus (with instructions on the mandatory part and supplementary material for each talk).

The talks are going to take place on Fridays 14:00-16:00 in room 0.003 at the University of Bonn and for the first three weeks also on Wednesdays in room SR 0.008 from 16:00 to 18:00.

Main references for the courses: [A] Akbulut. "4-manifolds". Oxford University Press. [GS] Gompf-Stipsicz "4-manifolds and Kirby calculus". American Mathematical Society, [DET] "The disc embedding theorem" (Edited by Stefan Behrens, Boldizsar Kalmar, Min Hoon Kim, Mark Powell, and Arunima Ray). Oxford University Press.

Topics in 4-manifolds. Seminar course coteached with Laura Wakelin. Summer semester 2024.

Download syllabus (with instructions on the mandatory part and supplementary material for each talk).

The talks are going to take place on Fridays 14:00-16:00 in room 0.003 at the University of Bonn and for the first three weeks also on Wednesdays in room SR 0.008 from 16:00 to 18:00.

Main references for the courses: [A] Akbulut. "4-manifolds". Oxford University Press. [GS] Gompf-Stipsicz "4-manifolds and Kirby calculus". American Mathematical Society, [DET] "The disc embedding theorem" (Edited by Stefan Behrens, Boldizsar Kalmar, Min Hoon Kim, Mark Powell, and Arunima Ray). Oxford University Press.

If you are a student preparing a talk read this.

For your talk it's fine to use slides if you want to. It's not mandatory but it's appreciated if you could send us your notes (even handwritten) even the day before your talk. Schedule at least one meeting with your examiner before your talk. It is fine spending the whole time talking about the mandatory part. It's up to you how to divide the time. If you are in doubt you can always write us an email.

Here are a few tips for your presentation.

Target: the target audience for your talk are your colleagues, not us examiners. In particular you should not assume that the audience is familiar with the results that you are going to talk about, the background can be mixed (topology or geometry). The goal is also to teach them the content of your talk.

When sketching a proof:

Summarizing the proof's idea or the principle behind it in a few words before digging into the proof it's always a good idea.
Tell people what's obvious (maybe special cases) and what is hard (at least what you have found hard).
Even if you are only sketching a proof, everything you decide to write on the blackboard has to be true and has to be precise (the audience shouldn't fill the gaps in your statements) modulo a few globally, obvious, implicit things.
It's OK to encapsulate a proof step in a proposition because it's too hard to prove it live, but in that case it should be remarked.
What is the mathematical technology that comes into the proof, who invented it?
Explain us if there are assumptions or properties which are false-friends: they seem to be obvious but are used in a non-obvious way
If you spent a lot of time to understand a step or the role of something, it's better to break it down for the audience even if it seems obvious to you now. Tell us those little, time-saving things that you want somebody had told you before you started studying that proof.
If you draw a picture, make it clear what it represents: is it our problem in one dimension less? Is it a different problem which has a similar solution? Is it an handle decomposition (in what dimension)? Is it just a schematic picture (no specific formalism involved)?
If you use a result or definition that has been introduced in another talk, than say so, it helps people recognizing it as something familiar.
It's often a good idea after you finish a multistep proof to summarize it verbally again.
Where did you use the assumptions of the thesis?
It's good to provide examples of applications and also examples of non-applications.
Give us references.
Help us examiners to understand how deep you studied.