February 26, 2007
Alan Hammond (NYU): The uncertainty principle
Abstract:
The uncertainty principle states that if a function is supported mainly
in a box of sidelength $\delta$, and its Fourier transform mainly in a
box of sidelength $\rho$, then $\delta \rho \geq 1$. The uncertainty
principle suggests a technique for bounding the number of eigenvalues
of an elliptic operator: instead of volume counting, which can lead to
wild over-estimates, we count the number of unit boxes that can
be symplectically embedded in phase space, thereby approximately
diagonalizing the operator. The embeddings must also satisfy certain
smoothness requirements. The talk is a presentation of a part of "the
uncertainty principle", C.Fefferman, Bull. Amer. Math. Soc.
(1983) no 2, 129-206.
back to the seminar homepage