**Israel Pollak Distinguished
Lecture Series**

A series of three lectures

will be presented by

**PROFESSOR SERGEY NOVIKOV
**University of Maryland and Landau
Institute for Physics

Member of the Russian Academy of Sciences

Fields Medalist

The lectures will be held in

Room 232

Amado Mathematics Building

Technion - Israel Institute of Technology

Haifa, Israel

Lecture I: Thursday, May 18, 2000 — 15:30

**OPERATORS ON GRAPHS
AND SYMPLECTIC GEOMETRY**

For the real self-adjoint Schrodinger operators on graphs,a homology-valued symplectic form (symplectic Wronskian) was invented in 1997. It plays a fundamental role in the construction of scattering theory for graphs with tails. A nonlinear extension of this quantity and some new aspects of the soliton theory will also be discussed.

Lecture II: Sunday, May 21, 2000 — 13:30

**EXACTLY SOLVABLE 2D
SCHRODINGER OPERATORS WITH MAGNETIC FIELD ON A LATTICE**

Non-standard "soliton-type" continuous and discrete symmetry transformations are used for finding a broad class of exactly solvable 2D Schrodinger operators in periodic fields, including topologically nontrivial cases.

Lecture III: Monday, May 22, 2000— 15:30

**QUASI-PERIODIC
FUNCTIONS ON THE PLANE AND TOPOLOGY**

The structure of levels of quasi-periodic functions on the plane with 3 periods leads to a highly nontrivial topological picture. It plays a fundamental role in the theory of metals. This problem has been studied from the topological point of view since 1982, and physical applications were found in 1996-99. New results have recently been obtained for functions with higher number of periods. It is hoped to find applications in the theory of quasi-crystals.