W. Dale Brownawell

Woodrow Dale Brownawell (born April 21, 1942 in Grundy County , Missouri ) is an American mathematician who studied number theory and algebraic geometry .

Brownawell is the son of a farmer. He studied German and mathematics at the University of Kansas with a bachelor's degree in both subjects in 1964 with top grades, then studied for a year as a Fulbright Fellow at the University of Hamburg and then at Cornell University and the State University of New York at Stony Brook (where he followed Schanuel in 1969), and received his PhD under Stephen Schanuel at Cornell University in 1970 ( Some Transcendence Results for the Exponential Function ). From 1970 he was Assistant Professor, from 1974 Associate Professor and from 1980 Professor at Pennsylvania State University , where he became Distinguished Professor and in 2013 he was retired.

In 1987 he gave upper bounds for the effective version of Hilbert's zero theorem , using analytical techniques that limited the validity to fields with the characteristic zero (in 1988 János Kollár then gave a purely algebraic proof, valid for any characteristic). Hilbert's zero theorem states that for a polynomial p in n variables over a field k, which vanishes on all common zeros of the elements of an ideal I in the polynomial ring (with variable values ​​in the algebraic closure K of k), a power is ideal. The effective version is about upper bounds for the degrees of the polynomials in the decomposition of after the base of the ideal. The upper bound found by Brownawell was exponential in the number of variables n. ${\displaystyle p^{r}}$ ${\displaystyle g_{i}}$ ${\displaystyle g=p^{r}=\sum _{i}f_{i}\cdot g_{i}}$ ${\displaystyle f_{i}}$

In 1986 he received the Hardy Ramanujan Prize with Michel Waldschmidt . Both independently proved the transcendence of at least one of the two numbers or (with Euler's number ). That solved a problem from Theodor Schneider about transcendent numbers . ${\displaystyle e^{e}}$ ${\displaystyle e^{e^{2}}}$ ${\displaystyle e}$

In 2012 he became a Fellow of the American Mathematical Society . In 1977/78 he received the Humboldt Research Award . In 1985/86 he was at the Institute for Advanced Study .

He met his wife Eva Brownawell during his time at the University of Hamburg. His hobbies include traveling and indoor roller skating.

Web links

• Homepage with CV

Individual evidence

1. ↑ W. Dale Brownawell in Mathematics Genealogy Project (English)
2. ↑ Brownawell, Bounds for the degrees in the Nullstellensatz, Annals of Mathematics, vol 126, 1987, pp 577-591
3. ^ Kollar, Sharp Effective Zero Set, Journal of the American Mathematical Society, Volume 1, 1988, pp. 963-975
4. ↑ Brownawell, The algebraic independence of certain numbers related by the exponential function, J. Number Theory, Volume 6, 1974, pp. 22-31
5. ^ Waldschmidt, Solution du huitième Problem de Schneider, J. Number Theory, Volume 5, 1973, pp. 191-202
6. ↑ Entry on IAS
7. ^ Faces of Penn State, 2005: W. Dale Brownawell , Penn State Science