Presenting half-baked results in a department seminar

Question

After having submitted my Ph.D. recently, I am working on a first solo paper (without my advisors). I have some interesting results, but, I have difficulty in formalizing some of the mathematical arguments. I tried to send the manuscript to some mathematicians for comments, and they said they will read it when they have time, but so far, apparently, they did not have time.

So, I scheduled a presentation in a local math department seminar. My hope is that, when people come to a seminar, they have more time to listen, and probably some of them will be able to help me. My concern is that, presenting such half-baked results might make me look unprofessional.

So, my question is: what is the best way to present such results in a way that will encourage interested listeners to collaborate with me, while not creating a negative impression?

Answer 1

Caveat: The following applies to venues where presenting work in progress is accepted, such as workshops or (as in this case) an internal department seminar. Of course, a high-ranking conference is not the right place for anything half-baked.

The idea is to explain at least those aspects very clearly that are not (as) "half-baked", while being honest about those that are half-baked.

• Make your research question very clear and explain why it matters. In the worst case, your audience can't comment on any of your half-baked findings, but then they can at least think with you about your research problem.
• Describe very clearly your analytical approach. Which methods/models/concepts/theories did you use to attack your problem? Help your audience to think about whether your analytical choices are useful and how they can be used to attack your problem.
• When it comes to your findings and their formalization, try to do a good job in their informal ("natural language") presentation. Perhaps you can already break down the finding analytically without going "fully formal". Then explicitly state that your current challenge is to formalize those findings. Show the audience briefly some angles that you have tried and where you got stuck. Explicitly and politely invite your audience to comment on the formalization.

The easier it is for your audience to understand your work, the easier it will be for them to help you with its formalization. This makes their comments more useful. At the same time, the better job you do at explaining clearly what you have done, what you know, and what you don't know, the more professional you come across.

Your goal is to make the audience think: "Hey, this guy has a very interesting and important puzzle. I think he also has a great model that explains it. I guess I should work with him on its formalization."

Answer 2

First, I am not sure what you mean by "half baked result". You have to be very clear about what results you actually have and which you only anticipate.

• If by half-baked result you mean "almost proven result", it is still a conjecture and should be presented as such. For a talk you should present results for which you have a clear proof (presenting the proof itself may not be a good idea depending on time and audience). If you have proofs of special cases of your "conjectures" listeners may be interested to collaborate on the proof of the conjecture.

• If by half-baked result you mean "results for which you have an informal proof" but no rigorous one, I am not sure, how to proceed. I would say, that a non-rigorous proof may count as "no proof" and the first bullet applies.