In this talk we consider real symmetric and complex Hermitian matrices depending on parameters, and are interested in detecting coalescence of their eigenvalues and locating where it occurs. This is an old problem (it traces back to a celebrated paper of von Neumann and Wigner (1929)) that has received much attention in various fields such as Physics, Chemistry and Engineering. We address both theoretical and numerical aspects of the problem, starting from the case of full "general" matrices and then moving to that of more structured (e.g. banded) matrices.
The talk is based on joint work with Luca Dieci (Georgia Inst. of Tech.) and Alessandra Papini (Univ. of Florence).