The Hilbert-Polya Conjecture and the Prolate Spheroidal Operator

One possible way of proving the famous and important Riemann hypothesis would be to realize the Riemann zeta zeroes as the eigenvalues of some self-adjoint operator, using self-adjointness to show that the non-trivial zeroes all lie on the critical line. This is known as the Hilbert-Polya conjecture. Interpreting such a self-adjoint operator as...

On the use of PCE based surrogate models in SXR Scatterometry

Scatterometry is a non-destructive metrology technique widely used in the semiconductor industry for the reconstruction of periodic structures from diffraction measurements. This involves solving a so-called inverse problem, which can be done by tuning the geometry parameters of a forward model such that the discrepancy between the measured...