Can I start such a contact with one researcher that does not know me in one online conference? I have a major in Mathematics and a masters in Physics and am currently starting my PhD in Physics. Since I've started my masters I am very interested in one particular research field. The main developments in this field have been carried out by a group lead by a very respected researcher. Moreover the book he wrote about the subject together with the papers of his group are what made me be interested in the field.
For my PhD I wanted to work with this field. My supervisor works in related stuff and he spent one year in the US doing his own research, but in a group that was actively discussing the subject I'm interested in, so that he got interested as well. In that case he accepted to supervise me. We are right now deciding on what to take as a concrete objective.
In that sense I had one particular idea that my supervisor really enjoyed and said it could really be the way to go. We are discussing now the particular details.
Now, I'm participating on one online conference and that physicist who leads the group which is making the most significant contributions to the field is participating. Moreover people say that he is approachable and there is one particular moment every day in the conference on which people are encouraged to talk to one another.
In that setting, I have been considering starting an interaction with that professor and ask him his view on the general idea of my proposal. In fact, in one of his papers there is one very short footnote briefly saying that one could perhaps do something related to what I have in mind, but his group followed a distinct direction.
Now while I think that trying to talk to him could be beneficial I fear whether or not I can do it and how to approach it in this online environment.
For starters he doesn't know me and we don't have any common acquaintances. Isn't it a bit of too much asking him privately in one online conference an opinion about an idea I had for my PhD project?
In that sense my question here is: can I try starting such an interaction? And if so how is the correct way to approach it given that he doesn't know me?
Conferences, including online ones, are for liaising with people and talking to them. There is nothing wrong with what you suggest. There is always the chance the professor might ignore you, not be interested or not know, but that can happen anyway.
I do not know what functionalities the conference offers, but a brief text or email asking if the professor could spare the time for a chat on X and Y seems like a good way to start. Try not to ask during the questions after a paper presentation or, generally, the proceedings of the conference, but a workshop might be an alternative. Personally, I would just text or email him.