This seminar was given as a pre-seminar. John Jones was due to give a series of seminars on Elliptic Cohomology in the Geometry Seminar Series at Warwick and so I gave this seminar in the Junior Geometry Series as an introduction aimed at a lower level than John's talks were going to be aimed at.

The plain for this seminar was to go through an example of Elliptic Cohomology in action. The example chosen is called the A-hat-genus. It is actually a degenerate case and so is not strictly an elliptic genus. However, it is still a good introductory example.