. DEPARTMENT of MATHEMATICS Structured Inverse Eigenvalue Problems Dr. Keivan Hassani Monfared Western Illinois University Abstract: Dynamical systems are everywhere, so too are the differential equations describing them. In this talk, rather than trying to find a solution to a systems of differential equations, in a combinatorial-matrix-theoretic approach we study what conditions on the expected behavior of a dynamical system guarantee the existence of a system with that given behavior. Certain behaviors of dynamical systems can be described by their natural frequencies, i.e. the eigenvalues of the coefficient matrix in the matrix form of the system of differential equations, where the coefficient matrix has a specific ’structure’. Such problems are called structured inverse eigenvalue problems (SIEP). Using the Jacobian method we show that for any given set L of n distinct real numbers, and any given graph G, there is a real symmetric matrix of order n whose graph is G, and its spectrum is L. Moreover, if G is connected, one can choose this matrix so that none of its eigenvectors have a zero entry. Thursday, October 30, 2014 3:45 p.m. Morgan Hall 204 Refreshments will be served at 3:30 p.m.