# Charles Fefferman

Wolf Prize Laureate in Mathematics 2017

**Charles Fefferman**

#### Affiliation at the time of the award:

**Princeton University, USA**

#### Award citation:

**“for their striking contributions to analysis and geometry”.**

#### Prize share:

**Charles Fefferman**

**Richard Schoen**

Charles Fefferman (born in 1949) evidenced an affinity for mathematics at an early age. As a 9-year-old in suburban Maryland, his interest in science fiction and rocketry led to a study of physics, and with it the desire to master the mathematics necessary to understand the physics textbooks he read. At age 12, he was being tutored by professors at the University of Maryland, where he matriculated at 14. He graduated in 1966 at the age of 17 with bachelor’s degrees in both mathematics and physics, earned with the highest distinction, having already published a paper on symbolic logic.

Fefferman earned his doctorate in mathematics in 1969 at Princeton University, supervised by Elias M. Stein, for a thesis entitled Inequalities for Strongly Regular Convolution Operators. After serving as a lecturer at Princeton for the 1969-1970 academic year, he took a position at the University of Chicago; one year later, in 1971, he was promoted to full professor there, making him the youngest full professor in the United States. In 1973 Fefferman returned to Princeton as a full professor, and was appointed the Herbert E. Jones ’43 Professor. He served as Chair of the Mathematics Department from 1999 to 2002.

Fefferman has been a dominant figure in analysis in the last 40 years, having made dramatic advances in a number of major new directions. It is no exaggeration to say that he is the most influential analyst of his generation. His major achievements include:

- He revolutionized our understanding of fundamental parts or real analysis by proving the duality of BMO with Hardy space H¹, whose results nowadays have innumerable applications.
- Fefferman made the first major breakthroughs in the areas related to Bochner-Riesz summability and restriction theorems, in finding a counter-example for the disc multiplier, and proving the first important positive results in this area.
- Fefferman’s study of the Bergman kernel and mapping properties of strongly pseudo-convex domains is a landmark in the field of several complex variables and has also opened the way for important geometric consequences.
- Fefferman obtained among the best results in the theory of pseudo-differential operators in the last 40 years:
- Resolving with Beals a fundamental open problem of local stability.
- Obtaining with Phong the optimal results for positive operators and sharp Garding inequalities.
- Achieving the decisive results for second-order non-negative sub-elliptic operators.

- In the last ten years he has obtained dramatic breakthroughs and important generalizations in the area of the Whitney extension problem. This fundamental work is contained in a series of works beginning with five papers in the
*Annals of Mathematics*from 2005 to 2009, and including more recently collaborations with B. Klartag, A. Israel, and K. Luli. It deals with the general problem of given a set E in Rn and a function f0 on E, when (and how) does it extend to a function f on Rn that belongs to a given Banach space X of “smooth” functions (e.g. when X = Ck).

**Charles Fefferman is awarded the Wolf Prize for making major contributions to several fields, including several complex variables, partial differential equations and subelliptic problems. He introduced new fundamental techniques into harmonic analysis and explored their application to a wide range of fields including fluid dynamics, spectral geometry and mathematical physics. This had a major impact on regularity questions for classical equations such as the Navier-Stokes equation and the Euler equation. He solved major problems related to the fine structure of solutions to partial differential equations.**