DISTINGUISHED LECTURE SERIES 1998/99

**Professor Elias M. Stein**

Princeton University Wolf Prize Recipient for 1999 Member of the National Academy of Sciences of the U.S.A.

will deliver a special series of three lectures on

**HARMONIC ANALYSIS**

Lectures will be held in Room 232, Amado Mathematics Building, Technion.

Light refreshments will be served in Room 820 before the lectures.

Lecture I Thursday, May 6, 1999 at 16:30

**DISCRETE ANALOGS IN HARMONIC ANALYSIS I**

Lecture II Sunday, May 9, 1999 at 16:30

**DISCRETE ANALOGS IN HARMONIC ANALYSIS II**

These two lectures will survey work done jointly with S. Wainger and more recently also with A. Magyar, in the study of discrete versions of some important operators in Rn Fourier analysis. Among these are singular Radon transforms, fractional integration, and spherical maximal averages. The key techniques used are those that originated in the "circle method " of Hardy and Littlewood, and have been applied in number theory and ergodic theory.

Lecture III Monday, May 10, 1999 at 15:30

**SOME GEOMETRICAL CONCEPTS ARISING IN HARMONIC ANALYSIS**

Extensions of the classical theory of singular integrals have involved a series of geometrical concepts, such as approximation by graded nilpotent Lie groups, and the resulting control metrics. Several recent applications (coming from complex analysis) have highlighted circumstances where there may be two different and conflicting metrics that arise naturally. This paradoxical situation can be resolved by passing to the product theory.