I'm currently in the stage of my PhD (in math) where I need to start discussing with my advisor about my PhD project and I'm wondering what kind of things am I allowed to say and which ones should I avoid. I want to know how should I manage my communications with them.
More concretely, to which extent can I decline or object about certain projects they may suggest? Is it appropriate for me to say that a project doesn't appeal me, or that I'd rather do something more [concrete, abstract, with more applications, etc.]? Is it reasonable to bring up the projects of my peers?
I've heard about people having their advisers proposing multiple projects from which they may decide, however, up until this point that doesn't seem to be my case. Otherwise I wouldn't be looking for advise. In any case, I understand they're experts in their area and their suggestions are very well thought (relative to me and the research area) and on-point.