Background: I am a fourth year math graduate student working in differential geometry in the US.
I'm currently preparing a presentation for a graduate seminar at my university, and today I met with my research advisor to go through my outline. Shortly into our discussion, he became rather serious and expressed concern about my inclusion of unfinished work and unexplored ideas. While they only make up about 5–10 minutes of my hour-long talk, he was worried that I'm not sufficiently protecting my IP from theft. He went on to say that this is a much more significant concern at conferences where I would know very little about my audience members, but he still wanted to exercise caution.
I don't disagree with him, but that led me with the following questions:
In my personal opinion, I work in a rather dark corner of my discipline. I don't intend to contradict my advisor, but is this a legitimate concern?
Obviously the risk is venue dependent, but would there be any forum in which I would be completely safe?
How nervous should I be to discuss ideas with people who ask questions at the conclusion of my presentation? Do people ever go "fishing" for ideas?
Should I be more careful speaking about "unfinished work" or "unexplored ideas"? Does one carry more danger than the other?
Since publishing is such a drawn out process, is there some point before the release of one's results that they could be given as part of a presentation?
Finally: Is there any way to say how much should I feel safe sharing?
Any responses to these questions or related comments are much appreciated.