Giving talks on ongoing, unpublished research (dangers of getting scooped?) In my school sometimes the graduate students have to give a talk on what they are up to, i.e. present their ongoing research. Often at this stage the work is not published yet. This is an internal event within the school, within the department. The audience are mainly other graduate students, and professors.

Are there any tips to give such a talk? More specifically, how to reduce the risk (if any) of getting scooped, and ideas stolen? The context is in the subject of mathematics/ mathematical sciences.

Thanks a lot.
Getting ideas stolen is a common fear when starting out (or at least all my Ph.D. students had that worry, and I did too when I was one) but it is much less common that one would think. While the risk does exist, the benefits of opening your research to get feedback from other people greatly outweigh it. Keeping your research secret is just not worth it.

In any case, if you want to reduce the risk, something that you can do is (paradoxically) open up even more! Announce the talk at your website, put your slides online, tweet about it, etc. This means that there will be publicly available evidence that you had ongoing research on topic X by date Y, so prospective scoopers would be easily exposed.