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I'm a postdoc in mathematics. I had a conversation with a professor after he gave a talk at my university, and he seemed interested in my ideas. I sent him an email the next day to elaborate on our discussion, and he replied by inviting me to give a talk at his university. I accepted the invitation.

However, I don't feel confident about giving a talk on the subject of our conversation. I wrote something about it in my thesis which I sent to him in my email, but it was just some undeveloped ideas (not central to the thesis), and I am certainly not an expert in that area. Is it okay to give a talk on a different topic?

He didn't specify what he wanted me to talk about, but we didn't discuss anything else than that, and it seems like our only point in common. So, I fear it would be awkward to give a talk on my true expertise area. Or is it?

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    what are you trying to achieve by giving this talk? Commented Nov 7, 2019 at 4:37
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    This is one of those cases where the only real answer is "ask the professor".
    – Mast
    Commented Nov 7, 2019 at 15:27
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    Is there anything stopping you from discussing this further with the professor to clarify your mutual understanding of what is desired and what you're comfortable doing?
    – Makyen
    Commented Nov 7, 2019 at 19:11

5 Answers 5

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If you haven't come to an agreement on what you would discuss, then I think you are pretty free. But as a courtesy, if nothing else, send him a note about your topic. If he disagrees you might want to re-think it.

However, a talk about partially unformed ideas, if presented that way can be very valuable. It can give ideas about research the listeners might explore. If you do it right, it can give ideas about how to come up with such ideas and how to begin to tackle them. What insight do you have into the problems?

In the best case it can lead to collaborations on that topic and others that might emerge from the exploration.

In fact, a talk on "things worth exploring" is probably more interesting to a mathematician than one on "things done and finished."

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As a courtesy to your audience and potential audience, as well as the professor, make sure the topic of your talk is accurately established well in advance. It is frustrating to go to a talk that is not on the stated topic and does not interest me, and to miss a talk that would have interested me if I had known what it was about.

I suggest discussing topic and title with the inviting professor as soon as possible.

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    Well, if it's interesting, then it's not frustrating.
    – Strawberry
    Commented Nov 7, 2019 at 11:12
  • +1 for "potential audience", referring to people who didn't have to show up just to realize that the topic is interesting but only for somebody other than themselves and whose own interest actually rested with the announced and/or incorrectly guessed topic. Commented Nov 8, 2019 at 17:05
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Another possible aspect of the situation is that the invitation to speak at the seminar is a way to fund a short visit on your part, in which you could discuss more with that professor. If that is the case, the topic of your talk wouldn't necessarily need to be the same as you discussed.

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I think this depends on who the audience for your talk is. Maybe he invited you because he wanted to hear some more about this particular topic and possibly have some joint research come out of it. The audience in that case would be his research group. If on the other hand this is a general seminar for his entire department it would be perfectly acceptable to talk about some topic you feel more comfortable with. Ask him who the audience is, what you both want to get from the talk and make a suitable decision.

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I think you're free to give a talk on any topic that you think is relevant to the audience. I've given several seminars while visiting other institutions and assist with organising them at our institute. The topic of a talk is rarely stipulated, although a speaker is usually expected to give a title or abstract ahead of time to promote the talk.

You can take the talk as an opportunity to introduce yourself, your skills, and wider research topics. It does not have to be restricted to the topic you are interested in working on in the future. You can, of course, have private meetings about other topics while you are there. It is up to you alone (and perhaps your co-authors) whether you share unpublished findings. What's most important it to bear in mind the audience and to focus on a few topics to allow enough time to go into detail rather than overloading with information. I think it's safe to assume that most academics have wider interests than what they are currently working on. If they've invited you or shown up to a talk announced about you, then they're interested to hear what you have to present.

You should think about what you want to get out of the talk. Some people give talks much like a conference but seminars can be more informal. If you are an early-career researcher, bear in mind that these may be people that could hire or collaborate with you in the future so do present yourself appropriately. Think about what topics you want to discuss with them afterwards and what you want them to know about your previous work. For some it's a chance to introduce yourself to the rest of the department. For others it's part of your job interview. The talk can be a formality to justify travel funds for other meetings or can be a courtesy to offer do do a talk while visiting. Content varies considerably accordingly.

What's most important is communication with your host who has invited you. If you have any doubts, then contact them. They'll rarely give you any conditions on what to talk about. You don't have to give them details in advance but it is polite to let them know your plans and interests ahead of time. If you give them enough notice, they can make sure that others that may be interested in your talk or meeting with you while you are there are available to do so. Please bear in mind that they may be very busy and need time to make arrangements, especially if they are covering the costs of your visit.

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