Amir Mohammadi (UC-San Diego)

The eigenvalues of the Laplacian on a generic 2-dimensonal flat torus are expected to behave like random numbers. In this talk we will report of a recent joint work with Lindenstrauss and Wang which establishes that the corresponding pair correlation function agrees with that of a Poisson process with a polynomial error rate, under explicit Diophantine condition to the torus. The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.