ar X iv : m at h - ph / 0 60 10 23 v 1 1 1 Ja n 20 06 Cardy ’ s Formula for Certain Models of the Bond – Triangular Type

ar X iv : m at h - ph / 0 60 60 44 v 1 1 9 Ju n 20 06 GEOMETRIC CURRENTS IN PIEZOELECTRICITY

As a simple model for piezoelectricity we consider a gas of infinitely many non-interacting electrons subject to a slowly time-dependent periodic potential. We show that in the adiabatic limit the macroscopic current is determined by the geometry of the Bloch bundle. As a consequence we obtain the King-Smith and Vanderbilt formula up to errors smaller than any power of the adiabatic parameter.

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

ar X iv : 0 90 7 . 20 23 v 1 [ m at h - ph ] 1 2 Ju l 2 00 9 Menelaus relation and Fay ’ s trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.

ar X iv : m at h - ph / 0 50 90 44 v 2 1 1 Ja n 20 06 RANDOM POLYNOMIALS , RANDOM MATRICES AND L - FUNCTIONS

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.

ar X iv : m at h - ph / 0 30 10 19 v 1 1 5 Ja n 20 03 Which distributions of matter diffract ? — Some answers