Nils Dencker

Nils Jonas Dencker (* 1953 in Lund ) is a Swedish mathematician who deals with partial differential equations.

Dencker received his doctorate in 1981 from Lund University under Lars Hörmander . As a post-doc he was a Moore Instructor at the Massachusetts Institute of Technology from 1981 to 1983 and was then a professor at Lund University.

He is chairman of the Swedish Mathematical Society (2008). In 2003 he received the Gaarding Prize.

In 2005 he received the Clay Research Award for his complete solution of a conjecture by François Treves and Louis Nirenberg from 1970, which provides a necessary and sufficient condition (called condition " ") of a geometrical nature for a pseudo differential operator of the main type to be locally solvable. The necessity of the condition was previously proven by R. Moyer (1978) and Hörmander (1981). Dencker's proof also provides an explanation for the then surprising discovery by Hans Lewy ( example from Lewy , 1957) of a linear partial differential operator that is not locally solvable in the sense of the above conjecture. ${\displaystyle \Psi }$

Dencker also investigated the propagation of vector-valued singularities of partial differential equations (with applications, for example, in the birefringence of polarized light).

In 2008 he was an invited speaker at the European Congress of Mathematicians in Amsterdam ( The solvability of differential equations ). In 2010 he was invited speaker at the International Congress of Mathematicians in Hyderabad ( The solvability of differential equations ). He is a Fellow of the American Mathematical Society and a member of the Royal Swedish Academy of Sciences .

Web links

• Homepage in Lund
• Nils Dencker in the Mathematics Genealogy Project (English)
• Portrait at the Clay Research Institute

Individual evidence

1. ^ The resolution of the Nirenberg-Treves Conjecture , Annals of Mathematics, Vol. 163, 2006, pp. 405-444