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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:

  1. 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?

  2. Obviously the risk is venue dependent, but would there be any forum in which I would be completely safe?

  3. 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?

  4. Should I be more careful speaking about "unfinished work" or "unexplored ideas"? Does one carry more danger than the other?

  5. 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?

  6. 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.

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    Why do you need include "unfinished work and unexplored ideas" on your talk. Don't you have enough to talk about your already published material? – Alexandros Nov 20 '15 at 16:07
  • I only have one publication, and it's from my REU. To be honest, I feel that this is quite common among graduate students in math, at least among those outside the very best schools. I'm at a school I'd consider to be pretty good, and there are only a handful of students here with any publications. – AegisCruiser Nov 21 '15 at 18:56
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tl;dr: Light is the best disinfection.

If you work in a relatively small sub-area, and know all your potential colleagues and collaborators, you can decide for yourself how likely is that some of them can "borrow" an idea from you and publish it as your own. Your personal intuition about your the situation in your particular case is much more relevant than a general discussion.

However, you can also consider the following facts to help you make your decision:

  1. Publishing process in Maths usually takes much longer than in Physics, Chemistry, Engineering, or related "hard" areas. It is not uncommon for an article to be in first review for 6-9 months, and it is not uncommon to have 2 or more review cycles. Are you really ready to keep your findings secret until the paper is published?
  2. If some ideas were shared among a small circle of colleagues, and two of them claim that they "own" the result, it is actually more difficult to find out, who was the original author, and who pretends to be one. On the contrary, if the pre-print is made public, and the ideas are presented on a large international conference (in a room with more than 10 people), than there are more witnesses who connect the idea with your name, and it is less likely that someone will dare to stole the authorship (but still possible, of course).
  3. An important task of your supervisor (as any supervisor) is to ensure that the work will be eventually published; and as you know publishing is time- and effort-demanding. By expressing their concern, your adviser in some form encourages you to publish these ideas as soon as possible, which is a completely legitimate request. In fact, if one shares a good idea on a conference, but then never publishes it, someone else definitely will, sooner or later.
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    You don't need to keep them to yourself until they are published, only until they are submitted (you can put them up on arXiv at that point, plus you will have a submission date to point to if something comes up). – Morgan Rodgers Nov 22 '15 at 9:47
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  1. Better safe than sorry -- think about how devastating it could be, if someone from that audience decides to explore with your ideas and publish before you can get your thesis out.

  2. No. Maybe in a group meeting with the other students of your advisor.

  3. You don't need to be too nervous. But do say clearly that you are working on a problem for your thesis, if someone comes too close to asking questions that you're exploring in your thesis. Again, I'm not suggesting that most mathematicians are jerks, but it's better to be safe than sorry.

  4. Yes. For two reasons. One, your ideas might get stolen (it's rare, but it does happen, and especially if you don't know who is in your audience, it's a gamble). Two, especially as a graduate student, people don't really believe you if you have all these grand ideas that you have not explored. Talking about unfinished work lowers your credibility.

  5. Only if you have a preprint on hand (ideally on arXiv). If the audience asks for a preprint, you should be ready to hand it to them. As you become more senior, you might be able to get away with not having a preprint, but as a graduate student, you should really have a preprint.

  6. Uh, only the stuff that you feel absolutely sure about. Don't spew out nonsense, because people can (sometimes) tell that you're bluffing. It's better not to take any chances when you're so early on in your career.

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