COLUMBIA UNIVERSITY Department of Mathematics     ELLIS R. KOLCHIN MEMORIAL LECTURES   Peter Sarnak Princeton University Eigen and L Functions on Arithmetic Surfaces     Abstract: The problem of understanding the behavior of high frequency eigenstates of the Laplacian on a surface of negative curvature is one of the central issues in quantum chaos.  In the case of an arithmetic hyperbolic surface these questions are closely connected to L-functions and there has been much progress recently.We will review the general problem and describe some recent results and methods. The address of the International Affairs Building: 420 West 118th Street Go to the 6th floor- Plaza Entrance Dag Hammarskjold Lounge   Tuesday, March 26 4:30 p.m.   Tea will be served at 3:30 p.m. - 508 Mathematics Building   Directions to Columbia University