Maciej Zworski, Department of Mathematics, University of Toronto, is the world's leading mathematician under the age of 40 in the difficult and fundamental area of mathematics connecting partial differential equations, mathematical physics and applied mathematics. His research provides works of reference and starting points for other mathematicians. The amazing progress in the understanding of resonances in the last ten years is due largely to Zworski. He settled a famous problem formulated by the physicist Regge thirty years ago. Zworski also found the precise location of the shadow boundary in the diffraction of linear oscillatory waves by a convex boundary, thus proving a long standing conjecture of Keller and Rubinow. This refines work dating back to the last century and was not known even on the level of formal expansions.