Conferences and workshops are often great – getting together and being together is an ideal setting for doing research and learning things. However, there are various reasons to encourage the possibility of having conferences and workshop through "cyber space". The cost of travel, in terms of time, money, $CO_2$, is large.
Q1: My first question is about software that makes it possible to run lectures with long-distance participation. What are the features and what are additional features we would like to see.
Q2 My second question is about what could be good ideas for running a long-distance workshops or conferences. (This question is mainly experience-based rather than opinion-based.) Hybrid setting with conventional conference that allows some participation from cyber space? Completely cyber conference where each participant stays in his office/study.?
I have some experience with the TCS+ seminars which are completely in cyberspace and participants from the audience can ask questions. They work rather well. (But only a few participants per talk.) I am not familiar of similar things in mathematics.
Very related question: Tools for long-distance collaboration (This is about tools for long distance collaboration, in general. Not specific to seminars/workshops/conferences and also asked nine years ago.)
Best Answer
In addition to the homotopy type theory seminar already mentioned, there is also the electronic Computational Homotopy Theory Seminar:
https://s.wayne.edu/isaksen/echt/
Every week, the audience consists of a physically present group, and others who use Zoom to connect. It's pretty seamless to click the link and join (no need for the organizer to manage who has access, etc). The organizer has the ability to mute all microphones, and then audience members can unmute themselves to ask a question. The organizer can presumably also kick people out (e.g., if someone got the link and was trying to be disruptive). Maybe you could reach out to Dan Isaksen for advice, as this seminar is very well organized and successful.
A group of homotopy theorists also published a paper about "less climate-impactful conferencing." This was after they ran a conference that had two hubs instead of one. You could imagine generalizing their model to regional hubs. Hope this helps!