The disastrous year we have experienced has brought with it new ways of relating to each other. In particular, in mathematics, we realized that we already had the tools to give talks 3000 miles away without leaving home. Numerous online seminars sprang up in the first months of the confinement and it is becoming increasingly clear that many of them are not going to die when this is all over. This whole development has been quite organic but at the same time a bit chaotic. For example: several seminars with exactly the same objective emerged at the same time, or suddenly seminars in one department of one university were frequented by researchers from all over the world, thus becoming de facto global forums for the transmission of our work as researchers.
What I intend to propose with this message is that we manage to extract the best of everything that has happened in the last year and, perhaps with a small collective effort, modify or complement the way in which we interact with each other.
I would like to make some concrete proposals that, in no case, are intended to replace the usual practices up to now (but rather to complement them):
The creation of global seminars in the style of https://www.maths.ed.ac.uk/cheltsov/zag/ for different areas of mathematics.
The seminars of 1) could be complemented with an online platform (which could be the same Mathoverflow) where the recorded videos of the talks are available (with the author’s authorization) and where a discussion can be generated about the talk itself. That is, at the end the video of the talk would be like a Mathoverflow post where people could ask questions (but not only during the 5 minutes after the talk!) and the community (not necessarily the author) could answer those questions.
Something similar to 2) but with each paper. That is, a researcher writes a new paper, uploads it to arxiv and records a video (in the style of a talk) telling about the paper. Then he/she uploads the video to the platform (or to a Mathoverflow post) and a discussion about the paper is generated.
I honestly don’t think this is too idealistic. I think it is something that is perfectly within our reach and that could generate new dynamics of collaboration, error correction and dissemination of the most cutting-edge ideas in each field.