PDF readers for presenting Math online In the current situation it seems especially important to be able to present your mathematical results online in a way that your audience does not fall asleep in front of their screens. But I am struggling to find suitable software one could use to enhance the usual beamer LaTeX presentations with some handwriting/drawing.
So I am searching for the following features:

*

*Allows to present PDFs, as generated by the beamer Latex package

*Compatibility with usual video conference software (should be easy, just share your screen)

*Easy to use and easy to access handwriting tools (pen, colors, laserpointer, etc.)

*Drawing should stay on the slide you drew them on, so you can go back to them and save them after your talk

*Program and Toolbar should not be visible to the audience (so maybe campatibility with 2 screens would be necessary here)

*Additionally: Shows next slide, time, additional notes, ... (only for the speaker)

What is the best tool you know for this purpose?
PS: I am not restricted to any operating system.
 A: For a couple of talks I borrowed an iPad and used the app Notability, which seems to cover most of what you wanted.

*

*I presented a PDF prepared with Beamer.

*The talk was through Zoom, which allows you to share an iPad screen connected through Airplay (or through a cable in theory, but I could not get this to work).

*I wrote with an Apple pencil and was happy with the options for different colours, styles etc that Notability provides, and the ease of accessing them during the talk. (Perhaps relevant here is to re-emphasize that this was borrowed equipment: I obviously practiced with it a little in advance, but not for so long, so this is some evidence that the learning curve is not steep).

*Notability is a note-taking app, and this process worked exactly as it would for annotating a PDF file, so annotations remain on the slide indefinitely once written. (In fact one feature that might have been helpful would be an easy way to clear all the annotations! I just imported the PDF again to a new Notability document.)

*Only the slides were visible to the audience, not the controls. (To clarify, by way of comparison with other answers: the controls were always visible to me.)

*I could not see things like the next slide or private notes, but I did not try to set this up, so maybe it is possible. I think I could probably see the time, but I am not 100% sure now.

As an audience member, I must say I have much preferred when speakers have not used Beamer, but written at least most things in real time like a board talk, although the lack of space and slow pace of writing with a stylus does make this rather difficult. (I did not even do it myself, despite this preference -- I had too many figures, and no previous experience using the stylus or the software, which put me off.) If you do this I think a feature to look for is the ability for the audience to see both the page you are writing on and the previous one, e.g. as two portrait pages side by side. I think Xournal can do this (and is especially on topic here because symplectic geometer Denis Auroux has some role in its development).
A: XODO PDF READER
Free to use. For the Windows version:

Allows to present PDFs, as generated by the beamer Latex package

Yes

Compatibility with usual video conference software (should be easy, just share your screen)

Yes

Easy to use and easy to access handwriting tools (pen, colors, laserpointer, etc.)

It is easy to write in a single color; it takes a few clicks to change it because the toolbar is not on the screen (as per your other request). I normally highlight the cursor with a button on my pen

Drawing should stay on the slide you drew them on, so you can go back to them and save them after your talk

Yes

Program and Toolbar should not be visible to the audience (so maybe campatibility with 2 screens would be necessary here)

Only the slides are visible. Tapping on the touchscreen shows a toolbar (pen and finger touches do different things; for instance you can move to the next slide with a flicker). I don't have a second screen on my tablet so I don't know if it supports it.

Additionally: Shows next slide, time, additional notes, ... (only for the speaker)

No.
A: If your presentation is based on a Beamer file, I recommend PdfPc. It supports a hidden dashboard for the speaker, showing previous/next slides and some annotation and pointing tools.
Moreover, it allows you to jump among sections without having to run slide by slide - which is particularly cumbersome when a single frame corresponds to multiple pages on the pdf file.
In practice, when using PdfPc you then would only share the presentation window (but not the speaker dashboard) on your video conferencing software.
