CMI recognizes Nils Dencker for his complete resolution of a conjecture made by F. Treves and L. Nirenberg in 1970. This conjecture posits an essentially geometric necessary and suffcient condition, "Psi", for a pseudo-differential operator of principal type to be locally solvable, i.e., for the equation Pu = f to have local solutions given a finite number of conditions on f. Dencker's work provides a full mathematical understanding of the surprising discovery by Hans Lewy in 1957 that there exist a linear partial differential operator -- a one-term, third-order perturbation of the Cauchy-Riemann operator -- which is not local solvable in this sense. The necessity of condition "Psi" was shown for operators in dimension 2 by R. Moyer in 1978 and in general by L. Hormander in 1981. The sufficiency of the condition has resisted many previous attacks.
Nils Dencker was born 1953 in Lund, Sweden. He received his Ph.D. from Lund University in 1981 under the direction of Lars Hormander. After spending 1981-1983 as a C.L.E. Moore instructor at MIT, he returned to Lund University. He has been the Director of Studies at the Department of Mathematics 2001-2003. Dencker received in 2003 the Gaarding prize from the Royal Physiographic Society in Lund. He is currently the vice chairman of the Swedish Mathematical Society.
Dencker's research interests lie in the microlocal analysis of partial differential equations and the calculus of pseudodifferential operators. He has studied the propagation of polarization (vector valued singularities) for systems of partial differential equations, for example in double refraction. Dencker has also studied the pseudospectra (spectral instability) of semi-classical partial differential equations and the solvability of partial differential equations.