Thomas Wolff (mathematician)

Thomas Hartwig Wolff (born July 14, 1954 in New York City , † July 31, 2000 in Kern County , California ) was an American mathematician who dealt with analysis .

Thomas Wolff (1992)

Wolff, the nephew of mathematician Clifford Gardner , studied at Harvard University (bachelor's degree 1975) and received his PhD in 1979 under Donald Sarason at the University of California, Berkeley (dissertation: Some Theorems on Vanishing Mean Oscillation ). As a post-doc he was at the University of Washington and the University of Chicago (from 1980 as a Fellow of the National Science Foundation). In 1982 he became an assistant professor at Caltech , where he later taught as a professor, except for the period 1986 to 1988 at the Courant Institute of Mathematical Sciences of New York University and 1992 to 1995 at Berkeley. He was also visiting professor at IHES (1990). In 1984 he became a research fellow of the Alfred P. Sloan Foundation ( Sloan Research Fellow ).

Wolff dealt in particular with harmonic analysis, but also partial differential equations, potential theory, complex analysis, geometric measurement theory. He already attracted attention with his dissertation, soon afterwards (1979) with his new, simpler proof of Lennart Carleson's Corona theorem (proved by him in 1962) in complex analysis, which was known to be notoriously difficult.

In 1986 he worked with Barry Simon on localization in quantum systems with randomly distributed potentials.

In 1985 he received the Salem Prize . In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (Generalizations of Fatou's theorem) and in 1998 in Berlin (Maximum averages and packing of one dimensional sets) . In 1999 he received the Bôcher Memorial Prize for his work on the Kakeya problem , which he approached using combinatorial methods, and harmonic measures . He and Peter Jones proved a long-standing assumption that harmonic measures in the plane only exist in dimension 1.

In 1995 he showed that the Minkowski dimension of a Besikowitsch set (which contains a segment of length 1 in every orientation) in n-dimensional Euclidean spaces is at least an important step towards proving the Kakeya conjecture . Its lower limit was later improved by Terence Tao and Nets Katz . ${\displaystyle {\frac {n+2}{2}}}$

He died in a car accident. Wolff was married to the mathematician Carol Shubin (professor at California State University, Northridge ) and had two sons.

Fonts

• Lectures on harmonic analysis, AMS 2003 (edited by Carol Shubin, Izabella Laba)

Web links

• Obituary, Notices AMS, May 2001, pdf, file
• Bocher Prize for Wolff, Notices AMS 1999, PDF file

Individual evidence

1. ↑ The family was also friends with Jürgen Moser , whom Wolff had known from his youth.
2. ↑ Thomas Wolff in the Mathematics Genealogy Project (English)
3. ↑ Not published by Wolff, but published in Paul Koosis: Introduction to Hp-spaces. With an appendix on Wolff's proof of the corona theorem. London Mathematical Society Lecture Note Series, Vol. 40, 1980.
4. ↑ Barry Simon, Thomas Wolff: Singular continuous spectrum under rank 1 perturbations and localizations for random hamiltonian systems , Comm. Pure and Applied Math., Vol. 39, 1986, p. 75
5. ↑ Generalizations of a problem of geometrical measurement theory originally posed by Kakeya: is there a surface of minimal content in which a needle of length 1 can be rotated 360 degrees?
6. ^ A Kakeya-type problem for circles , American Journal of Mathematics, Vol. 119, 1997, pp. 985-1026, An improved bound for Kakeya-type maximal functions , Rev. Mat. Iberoamericana, Vol. 11, 1995, pp. 651
7. ↑ Counterexamples with harmonic gradients in , Essays in Honor of Elias Stein, Princeton Math. Series, Vol. 42, 1995 p. 321 ${\displaystyle R^{3}}$
8. ^ Haussdorff dimension of harmonic measures in the plane , Acta Mathematica, Vol. 161, 1988, p. 131
9. ^ Wolff An improved bound for Kakeya type maximal functions , Rev. Mat. Iberoamericana, Volume 11 1995, pp. 651-674