Abstract: Let L be a line on a smooth Riemann surface. In the study of the Quantum Hall Effect on a Riemann surface we consider the wave functions given by the holomorphic sections of the p-tensor powers of a positive line bundle. The partition function is the square of the $L^2$-norm of the Slater determinant built with the help of a basis of such sections. We will explain some mathematic problems related to QHE. In particular, we will consider Fekete configurations, which are systems of points maximizing the pointwise norm of the Slater determinant. We will explain the convergence speed of the probability measure of the Fekete configurations, this result holds for any projective manifold.
