You may find the following points useful when preparing your talk.

Talk Guidelines

• The most important thing is that everybody in the audience takes something away from your talk.
• Emphasise what it is about your topic that is interesting and important to be working on, what is the motivation?
• Give the kind of talk you would like to hear.
• If you go into technical detail, ask yourself what precisely is important for the audience to understand and remember. Try to limit the number of different mathematical symbols you introduce, and make it easy for people to remember what they each represent.
• There is a lot more advice online on how to give good math talks e.g. by David Tong, Robert Geroch and Paul Halmos, http://xkcd.com/547/ (do a mouse-over for the last one)

The Audience

Your group will consist mainly of PhD students in neighbouring areas. They will have a similar level and similar interests, but possibly a different background to yourself. They are likely to have done comparable courses at advanced undergraduate and master's level and widely different stuff since then. You might like to read other people's abstracts while preparing your talk. The session Chairs will be happy to answer any more specific questions.

Accessible Talks

In each session there will also be one talk of more general interest, which we will advertise to current Part III and undergraduate students. For these you should assume very little previous knowledge. Concepts and notation you find extremely familiar may not have been met, and detailed calculations probably won't be necessary. You might want to decide on a few key points to make during the talk, and cover them well. Thanks to all of you giving these talks.