Marco Aldi (VCU)
On Weil's proof of the Plancherel Theorem.
In 1910 Plancherel proved that Fourier transform is an isometry on the space of square-integrable functions. In 1953 Weil gave a new proof, using the representation theory of the Heisenberg group. The goal of this talk is to present Weil's proof, emphasizing its geometric flavor. If time permits, a generalization arising in the quantization of loop spaces will be presented. This talk is intended to be accessible to graduate and advanced undergraduate students.