Anthony Henderson University of Sydney Fourier transform and Kloosterman sums. Friday 18th October, 12-1pm, Carslaw 373. Fourier transform on vector spaces over a finite field is defined as over the reals, using a sum instead of an integral. An interesting application of it was discovered by Springer: if your vector space is the dual of a Lie algebra, and you take the Fourier transform of the indicator function of a strongly regular coadjoint orbit, the result has a lot in common with the generic characters of the corresponding group. I will give an easy introduction to this idea, and suggest how a similar procedure might help in computing certain trigonometric sums which generalize Kloosterman sums.