Best practices when hosting visiting speaker (especially with the questions part of their talk)

I'm an undergrad and I have invited a speaker to come and speak in my department. He's a mathematician at another university, and although what he will talk about is relevant to mathematics, it's not an academic talk or seminar. It is an academic speaking to other academics and students in an academic setting, however.

I've organised this completely alone so it's down to me to introduce the speaker and make sure the talk runs smoothly. I've never done anything like this and I'm worrying about how I should do it. I'm especially worried about how to run the questions section - which will be a substantial part of the time (at least 15 minutes of the hour).

Here is how I imagine it should go:

• I thank people for coming and introduce the speaker.


• I sit down and the speaker... speaks.


• At the end of his talk I stand up and ask if there are any questions. If people raise their hands I'll point at them so they can ask the speaker their question. I'll keep an eye on the time so when there are just a few minutes left I'll say "there's time for just a couple more questions".


• After the last question, I'll thank the speaker again and that'll be it.

Should I be doing the questions? Or should I let him call on people himself? (In the latter case, how should I make sure we stay in the time limit?). Where should I stand if I'm moderating the questions? The lecture theatre has a stage where he will stand to give the talk. Should I just stand to the side of him? If I'm standing up there, is it ok for me to ask questions (particularly if nobody in the audience is doing so)?

This is in the UK, in case that's significant.